US8453498B2 - Actuatable capacitive transducer for quantitative nanoindentation combined with transmission electron microscopy - Google Patents

Abstract

An actuatable capacitive transducer including a transducer body, a first capacitor including a displaceable electrode and electrically configured as an electrostatic actuator, and a second capacitor including a displaceable electrode and electrically configured as a capacitive displacement sensor, wherein the second capacitor comprises a multi-plate capacitor. The actuatable capacitive transducer further includes a coupling shaft configured to mechanically couple the displaceable electrode of the first capacitor to the displaceable electrode of the second capacitor to form a displaceable electrode unit which is displaceable relative to the transducer body, and an electrically-conductive indenter mechanically coupled to the coupling shaft so as to be displaceable in unison with the displaceable electrode unit.

Description

CROSS-REFERENCE TO RELATED APPLICATION

This Utility patent application is a Divisional application of U.S. patent application Ser. No. 11/672,489, filed Feb. 7, 2007, which claims benefit from U.S. Provisional Patent Application No. 60/771,560, filed Feb. 8, 2006, priority to which is claimed under 35 U.S.C. §119(e) and which are both incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention may be related to work done with Government support under Grant No. DE-FG02-04ER83979 awarded by the Department of Energy.

BACKGROUND

Each reference from the following list of references is incorporated herein by reference:

• 1. A. C. Fischer-Cripps,Nanoindentation(Springer, New York, 2004). (“Reference 1”)
• 2. “Review of instrumented indentation”, M. R. VanLandingham,J. Res. Natl. Inst. Stand. Technol.108, 249 (2003). (“Reference 2”)
• 3. “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation measurements”, W. C. Oliver and G. M. Pharr,J. Mater. Res.7, 1564 (1992). (“Reference 3”)
• 4. “Challenges and interesting observations associated with feedback-controlled nanoindentation”, O. L. Warren, S. A. Downs, and T. J. Wyrobek,Z. Metallkd.95, 287 (2004). (“Reference 4”)
• 5. For a recent review of in-situ TEM techniques: “New developments in transmission electron microscopy for nanotechnology”, Z. L. Wang,Adv. Mater.15, 1497 (2003). (“Reference 5”)
• 6. “Development of an in situ nanoindentation specimen holder for the high voltage electron microscope”, M. A. Wall and U. Dahmen,Microsc. Microanal.3, 593 (1997). (“Reference 6”)
• 7. “An in situ nanoindentation specimen holder for a high voltage transmission electron microscope”, M. A. Wall and U. Dahmen,Microsc. Res. Tech.42, 248 (1998). (“Reference 7”)
• 8. “Development of a nanoindenter for in situ transmission electron microscopy”, E. A. Stach, T. Freeman, A. M. Minor, D. K. Owen, J. Cumings, M. A. Wall, T. Chraska, R. Hull, J. W. Morris, Jr., A. Zettl, and U. Dahmen,Microsc. Microanal.7, 507 (2001). (“Reference 8”)
• 9. “Quantitative in situ nanoindentation in an electron microscope”, A. M. Minor, J. W. Morris, and E. A. Stach,Appl. Phys. Lett.79, 1625 (2001). (“Reference 9”)
• 10. “In-situ transmission electron microscopy study of the nanoindentation behavior of Al”, A. M. Minor, E. T. Lilleodden, E. A. Stach, and J. W. Morris, Jr.,J. Electr. Mater.31, 958 (2002). (“Reference 10”)
• 11. “In-situ nanoindentation—a unique probe of deformation response in materials”, A. Minor, E. Lilleodden, M. Jin, E. Stach, D. Chrzan, B. Morris, T. Friedmann, X. Xiao, J. Carlisle, and O. Auciello,Microsc. Microanal.9, 900 (2003). (“Reference 11”)
• 12. “An in-situ TEM nanoindenter system with 3-axis inertial positioner”, M. S. Bobji, C. S. Ramanujan, R. C. Doole, J. B. Pethica, and B. J. Inkson,Mater. Res. Soc. Symp. Proc.778, U4.5.1 (2003). (“Reference 12”)
• 13. “Direct observations of incipient plasticity during nanoindentation of Al”, A. M. Minor, E. T. Lilleodden, E. A. Stach, and J. W. Morris, Jr.,J. Mater. Res.19, 178 (2004). (“Reference 13”)
• 14. “Dislocation-grain boundary interactions in martensitic steel observed through in situ nanoindentation in a transmission electron microscope”, T. Ohmura, A. M. Minor, E. A. Stach, and J. W. Morris, Jr.,J. Mater. Res.19, 3626 (2004). (“Reference 14”)
• 15. “Effects of solute Mg on grain boundary and dislocation dynamics during nanoindentation of Al—Mg thin films”, W. A. Soer, J. Th. M. De Hosson, A. M. Minor, J. W. Morris, Jr., and E. A. Stach,Acta Mater.52, 5783 (2004). (“Reference 15”)
• 16. “Study of deformation behavior of ultrafine-grained materials through in situ nanoindentation in a transmission electron microscope”, M. Jin, A. M. Minor, D. Ge, and J. W. Morris, Jr.,J. Mater. Res.20, 1735 (2005). (“Reference 16”)
• 17. “Room temperature dislocation plasticity in silicon”, A. M. Minor, E. T. Lilleodden, M. Jin, E. A. Stach, D. C. Chrzan, and J. W. Morris, Jr.,Philos. Mag.85, 323 (2005). (“Reference 17”)
• 18. “Indentation mechanics of Cu—Be quantified by an in situ transmission electron microscopy mechanical probe”, M. S. Bobji, J. B. Pethica, and B. J. Inkson,J. Mater. Res.20, 2726 (2005). (“Reference 18”)
• 19. Brochure from Gatan Inc. titled “In situ probing: STM-TEM systems from Nanofactory™ Instruments”. (“Reference 19”)
• 20. Presentation from Gatan Inc. titled “TEM-nanoindentor system from Nanofactory”, authored by Oleg Lourie, Gatan Inc. (“Reference 20”)
• 21. ISO 14577-1:2002 (“Metallic materials—instrumented indentation test for hardness and materials parameters—part 1: test method”); ISO 14577-2:2002 (“Metallic materials—instrumented indentation test for hardness and materials parameters—part 2: verification and calibration of testing machines”); ISO 14577-3:2002 (“Metallic materials—instrumented indentation test for hardness and materials parameters—part 3: calibration of reference blocks”). (“Reference 21”)
• 22. “Effect of PZT and PMN actuator hysteresis and creep on nanoindentation measurements using force microscopy”, S. M. Hues, C. F. Draper, K. P. Lee, and R. J. Colton,Rev. Sci. Instrum.65, 1561 (1994). (“Reference 22”)
• 23. “The effect of instrumental uncertainties on AFM indentation measurements”, M. R. VanLandingham,Microsc. Today97, 12 (1997). (“Reference 23”)
• 24. “Quantification issues in the identification of nanoscale regions of homopolymers using modulus measurement via AFM nanoindentation”, C. A. Clifford and M. P. Seah,Appl. Surf. Sci.252, 1915 (2005). (“Reference 24”)
• 25. “A micromachined nanoindentation force sensor”, A. Nafari, A. Danilov, H. Rödjegård, P. Enoksson, and H. Olin,Sens. Actuators, A,123-124, 44 (2005). (“Reference 25”)
• 26. Brochure from Hysitron, Inc. titled “TriboIndenter®: nanomechanical test instruments”; brochure from Hysitron, Inc. titled “Ubi 1®: scanning quasistatic nanoindentation”; brochure from Hysitron, Inc. titled “TriboScope®: quantitative nanomechanical testing for AFMs”. (“Reference 26”)
• 27. “A new force sensor incorporating force-feedback control for interfacial force microscopy”, S. A. Joyce and J. E. Houston,Rev. Sci. Instrum.62, 710 (1991). (“Reference 27”)
• 28. “Interfacial force microscopy: a novel scanning probe technique for imaging and quantitative measurement of interfacial forces and nanomechanical properties”, O. L. Warren, J. F. Graham, and P. R. Norton,Phys. Can.54, 122 (1998). (“Reference 28”)
• 29. “Apparatus for microindentation hardness testing and surface imaging incorporating a multi-plate capacitor system”, W. A. Bonin, U.S. Pat. Nos. 5,553,486 and 6,026,677. (“Reference 29”)
• 30. “Capacitive transducer with electrostatic actuation”, W. A. Bonin, U.S. Pat. No. 5,576,483. (“Reference 30”)
• 31. “Multi-dimensional capacitive transducer”, W. A. Bonin, U.S. Pat. Nos. 5,661,235 and 5,869,751. (“Reference 31”)
• 32. “Nanoindentation and picoindentation measurements using a capacitive transducer system in atomic force microscopy”, B. Bhushan, A. V. Kulkarni, W. Bonin, and J. T. Wyrobek,Philos. Mag. A74, 1117 (1996). (“Reference 32”)
• 33. For example: “Vertical comb-finger capacitive actuation and sensing for CMOS-MEMS”, H. Xie and G. K. Fedder,Sens. Actuators, A95, 212 (2002). (“Reference 33”)
• 34. “Force-sensing system, including a magnetically mounted rocking element”, J. E. Griffith and G. L. Miller, U.S. Pat. No. 5,307,693. (“Reference 34”)
• 35. “A rocking beam electrostatic balance for the measurement of small forces”, G. L. Miller, J. E. Griffith, E. R. Wagner, and D. A. Grigg,Rev. Sci. Instrum.62, 705 (1991). (“Reference 35”)
• 36. “High-resolution capacitive load-displacement transducer and its application in nanoindentation and adhesion measurements”, N. Yu, W. A. Bonin, and A. A. Polycarpou,Rev. Sci. Instrum.76, 045109 (2005). (“Reference 36”)
• 37. “Tapping mode imaging with an interfacial force microscope”, O. L. Warren, J. F. Graham, and P. R. Norton,Rev. Sci. Instrum.68, 4124 (1997). (“Reference 37”)
• 38. “Nanoindentation and contact stiffness measurement using force modulation with a capacitive load-displacement transducer”, S. A. S. Asif, K. J. Wahl, and R. J. Colton,Rev. Sci. Instrum.70, 2408 (1999). (“Reference 38”)
• 39. “Quantitative imaging of nanoscale mechanical properties using hybrid nanoindentation and force modulation”, S. A. S. Asif, K. J. Wahl, R. J. Colton, and O. L. Warren,J. Appl. Phys.90, 1192 (2001);Erratum90, 5838 (2001). (“Reference 39”)
• 40. “High-performance drive circuitry for capacitive transducers”, W. Bonin, U.S. Pat. No. 6,960,945. (“Reference 40”)

Nanoindentation (seeReferences 1 and 2), today's primary technique for probing small volumes of solids for the purpose of quantifying their mechanical properties, involves the use of an instrument referred to as a nanoindenter to conduct a nanoindentation test. At a minimum, a nanoindentation test entails a gradual loading followed by a gradual unloading of a sharp indenter against a sample. The indenter is usually made of diamond, diamond being both the stiffest and the hardest known material. The indenter is shaped to a well-defined geometry typically having an apical radius of curvature in the range of 50-100 nm. The most prevalent indenter geometry is the three-sided pyramidal Berkovich geometry, which imposes a representative strain of ˜7% if perfectly formed.

A hallmark of nanoindentation is the acquisition throughout the nanoindentation test of both the force applied to the sample (peak load typically <10 mN) and the indenter displacement into the sample (maximum penetration depth typically <10 μm) to generate a force-displacement curve. High-performance nanoindenters exhibit force and displacement noise floors below 1 μN RMS and 1 nm RMS, respectively. The sample's mechanical properties, such as elastic modulus and hardness, can be evaluated by analyzing the force-displacement curve, the most common method of analysis being the elastic unloading analysis published by Oliver and Pharr (see Reference 3) in 1992.

Nanoindentation suffers from a major shortcoming, however. Despite more than a decade's worth of maturation, nanoindentation still leaves much to be desired in terms of providing definitive mechanistic explanations for certain features of its outputted force-displacement curves. For example, the commonly observed load-controlled nanoindentation phenomenon of a pop-in transient (see Reference 4), a sudden sizeable increase in penetration depth without a corresponding increase in load, an event signaling discontinuous yielding, has many possible interpretations: dislocation burst, shear band formation, fracture onset, spalling, stress-induced phase transformation, etc. Because it is extremely difficult to image such discrete nano-to-atomistic scale happenings at their moments of occurrence, it is not surprising that the scientific literature is replete with examples of deformation mechanisms assigned to pop-in transients with little more to go on than knowledge of the nature of the sample under investigation in combination with educated speculation. The invention provides the opportunity to make unambiguous the microscopic origin of a pop-in transient, or that of any other encountered nanoindentation phenomenon, by coupling nanoindentation to a TEM in an in-situ manner (see Reference 5). Doing so required meeting a set of configurational and environmental challenges not anticipated by existing nanoindentation transducers.

Configurational challenges presented by TEMs include: (1) severely restricted space mandating a nanoindentation transducer considerably more miniature than those currently supplied with commercial nanoindenters; (2) achieving acceptably high maximums in load and penetration depth in spite of the limited size of the transducer; (3) the need to operate the transducer with its indenter horizontal rather than in the standard vertical orientation; (4) the requirement that the indenter extend significantly from the transducer's body to reach well into the TEM's pole piece gap, which necessitates means for countering the associated tilting moment; (5) the requirement that the transducer be largely insensitive with respect to being rotated about the indenter's axis; and (6) the requirement that the transducer achieve high performance in spite of long wiring runs from the transducer residing in vacuum to its electronic circuitry residing out of vacuum, the longer the wiring runs, the greater the likelihood of electromagnetic interference pick-up and capacitive signal loading.

Environmental challenges presented by TEMs include: (1) high vacuum (e.g., 10⁻⁷torr) limiting construction materials to those not prone to outgassing; (2) the requirement that the transducer not seriously impede the pumping conductance of the TEM holder so that high vacuum can be achieved in a sensible period of time; (3) high vacuum restricting actuation/sensing strategies to those generating minimal heat; (4) high vacuum increasing the transducer's mechanical quality factor (Q) to a value much higher than in air, the higher the quality factor, the longer the impulse-ring-down time; (5) the presence of a highly energetic electron beam (e.g., 300 kV) impinging the indenter, which necessitates means for bleeding charge from the indenter; and (6) the presence of an especially strong magnetic field (e.g., 2 tesla in magnitude) restricting actuation/sensing strategies to those not relying on magnetic principles, and limiting construction materials to those without ferromagnetic content.

Owing to the severe set of challenges to overcome, previous attempts at in-situ TEM nanoindentation (see References 6-20) have been limited to qualitative or semi-quantitative experimentation. Qualitative in-situ TEM nanoindentation refers to viewing/recording a stream of TEM images that show how a sample deforms during the nanoindentation process without having the technology to acquire a corresponding force-displacement curve. The inability to acquire a force-displacement curve renders this experimental approach of low relevance to the invention. Semi-quantitative in-situ TEM nanoindentation also refers to viewing/recording a stream of TEM images that show how a sample deforms during the nanoindentation process, but with the added dimension of acquiring a corresponding force-displacement curve of poor accuracy relative to metrological standards established for nanoindentation, such as those expressed in ISO 14577 (see Reference 21).

Further discussion of semi-quantitative nanoindentation helps to clarify the meaning of quantitative nanoindentation (quantitative nanoindentation is often referred to as depth-sensing indentation). The in-situ TEM nanoindenter manufactured by Nanofactory Instruments AB (TEM-Nanoindentor: SA2000.N (see References 19 and 20)) is a highly relevant example of a semi-quantitative nanoindenter. Nanofactory's instrument is at odds with metrological standards established for nanoindentation on account of the series loading configuration it adopts. The series loading configuration poses a problem because it does not provide a direct measure of penetration depth. Instead, ignoring factors such as load frame compliance and thermally-induced relative position drift, the penetration depth is equal to the motion provided by an actuator minus the deflection associated with a device inferring load. The change in deflection is virtually equal to the change in motion in the limit of high contact stiffness, where “high” means high relative to the spring constant of the deflectable device inferring load. Consequently, it is virtually impossible to resolve changes in penetration depth in the high contact stiffness limit, a limit very easily reached. In contrast, quantitative nanoindenters exhibit constant penetration depth resolution regardless of the value of the contact stiffness.

To further complicate matters, Nanofactory's instrument relies on a piezoelectric actuator to affect the indenter-sample separation, but the instrument does not have a displacement sensor dedicated to measuring the actuator's extension or contraction (see Reference 20). Computing a piezoelectric actuator's extension or contraction from the voltage applied to the actuator has been shown to be unreliable because such actuators exhibit non-linearity, hysteresis, and creep dependent on the history of use (see Reference 22). Sequential analysis of TEM images that show the indenter penetrating the sample seems to be a viable way of directly quantifying the penetration depth in the absence of direct depth sensing. However, our own experience tells us this method is inconvenient and of dubious accuracy. Moreover, the indenter cannot be seen in dark-field TEM images. Operationally, Nanofactory's instrument is reminiscent of an atomic force microscope (AFM) conducting nanoindentation. There is a long history of AFMs delivering faulty force-displacement curves partially on account of the difficulties just mentioned (see References 23 and 24).

In Nanofactory's instrument, the deflectable device inferring load is a miniature two-plate capacitive transducer (see Reference 25) comprising a stationary electrode and a spring-supported displaceable electrode to which the indenter is attached perpendicularly; “stationary” and “displaceable” mean stationary and displaceable with respect to the transducer's body. The displaceable electrode's deflection is determined by monitoring the change in capacitance. Multiplying the displaceable electrode's deflection by the spring constant of the springs supporting the displaceable electrode yields the force acting on the indenter. Curiously, Nanofactory's instrument does not capitalize its potential for electrostatic actuation (see Reference 20), which prevents it from employing a loading configuration other than the inappropriate series loading configuration.

A suite of nanoindenters manufactured by Hysitron, Inc. (see Reference 26) and the interfacial force microscope (IFM) (see References 27 and 28) originating from Sandia National Laboratories are scanning nanoindenters utilizing actuatable capacitive transducers. Both types of instruments are capable of raster scanning the indenter to image a sample's surface in the manner of an AFM. Useful information regarding deformation mechanisms can be obtained from post-test images of the indent's topography, but such images illustrate no more than the residual deformation field.

At the heart of Hysitron's nanoindenters is a patented three-plate capacitive transducer (see References 29-32) comprising two stationary electrodes and a spring-supported displaceable electrode to which the indenter is attached perpendicularly; “stationary” and “displaceable” mean the same as before. The electrodes are components of a three-plate stack, the displaceable electrode being an element of the center plate. Each stationary electrode has a center hole, one center hole passing through the indenter without hindrance and the other center hole with the purpose of equalizing electrode areas. The dual capability of electrostatic actuation and capacitive displacement sensing is a hallmark of Hysitron's three-plate capacitive transducer. Electrostatic actuation in this case refers to generating an electrostatic force between the displaceable electrode and the stationary electrode through which the indenter passes, which deflects the displaceable electrode with respect to the stationary electrodes. Capacitive displacement sensing in this case refers to sensing the deflection using the well-established differential capacitance half-bridge method involving all three electrodes now widely adopted by microelectromechanical systems (MEMS) (see Reference 33).

Hysitron's nanoindenters adopt a parallel loading configuration, meaning contact stiffness in parallel with the spring constant of the support springs. This loading configuration results in the transducer's capacitive displacement sensing output providing a direct measure of penetration depth, again ignoring factors such as load frame compliance and thermally-induced relative position drift. The calculation of contact force involves the applied electrostatic force and the spring force, the spring force being related to the product of the easily-calibrated spring constant of the support springs and the displaceable electrode's deflection.

At the heart of the IFM is a differential-capacitance displacement sensor (see Reference 27) (IFM sensor for brevity) comprised of two co-planar stationary electrodes facing a torsion-bar-supported rotatable electrode; “stationary” and “rotatable” mean stationary and rotatable with respect to the sensor's body. The rotatable electrode together with a pair of torsion bars extending from opposing edges of the rotatable electrode resembles a torsional pendulum. The indenter is attached perpendicularly to the outer face of the rotatable electrode at a position equivalent to one stationary electrode's center. A hallmark of the IFM is its operation as a torque balance. An electrostatic-force-feedback controller is used to servo the indenter-side electrostatic torque to continuously suppress the rotatable electrode from rotating under the influence of the indenter-sample torque; the non-indenter-side electrostatic torque is held constant by the controller. The well-established differential capacitance half-bridge method involving all three electrodes is used to sense the rotational displacement of the rotatable electrode. But the action of the controller continuously nulls the sensor's capacitive displacement sensing output. The rocking beam sensor (seeReferences 34 and 35) originating from Bell Laboratories is similar to the IFM sensor, but is used for critical dimensional metrology rather than for nanoindentation.

IFMs use a piezoelectric actuator to affect the indenter-sample separation. The motion provided by the piezoelectric actuator in combination with the stiffening action of the electrostatic-force-feedback controller permits direct control of penetration depth, once more ignoring factors such as load frame stiffness and thermally-induced relative position drift. IFMs currently do not have a displacement sensor dedicated to measuring the piezoelectric actuator's extension or contraction; nevertheless, IFMs are quantitative nanoindenters from the viewpoint of loading configuration. Solving the relevant torque balance equation yields the contact force. The rotational spring constant of the torsion bars does not enter into the calculation of contact force because the rotatable electrode is suppressed from rotating.

The IFM sensor is currently too large to be housed in a TEM holder; furthermore, the baseline control effort needed to maintain an extended-length indenter in the horizontal orientation will be highly dependent on TEM-holder rotation angle, as will be the maximum load available for nanoindentation. Nevertheless, actuatable capacitive transducers are highly attractive for quantitative in-situ TEM nanoindentation because their operation is not based on magnetic principles, they draw very little electrical current, thus they generate very little heat, and they possess favorable scaling laws for miniaturization.

The Detailed Description of the invention discloses a novel actuatable capacitive transducer in addition to other novel aspects of the invention. Yu et al. made an initial public disclosure on an alternative actuatable capacitive transducer in the on-line version ofReference 36 on Mar. 28, 2005. The Yu et al. alternative actuatable capacitive transducer clearly is not suitable for quantitative in-situ TEM nanoindentation as disclosed.

For these and other reasons there is a need for the present invention.

SUMMARY

One aspect of the present invention relates to an actuatable capacitive transducer which enables quantitative in-situ nanoindentation in a transmission electron microscope (TEM). The quantitative in-situ TEM nanoindentation technique involves indenting a sample to acquire a quantitative force-displacement curve and simultaneously viewing/recording a stream of TEM images that show how the sample deforms while being indented. This simultaneous capability permits, for example, a direct correlation of a specific transient feature of the force-displacement curve to the sample's sudden change in microstructure.

In one embodiment, the present invention provides an actuatable capacitive transducer including a transducer body, a first capacitor including a displaceable electrode and electrically configured as an electrostatic actuator, and a second capacitor including a displaceable electrode and electrically configured as a capacitive displacement sensor, wherein the second capacitor comprises a multi-plate capacitor. The actuatable capacitive transducer further includes a coupling shaft configured to mechanically couple the displaceable electrode of the first capacitor to the displaceable electrode of the second capacitor to form a displaceable electrode unit which is displaceable relative to the transducer body, and an electrically-conductive indenter mechanically coupled to the coupling shaft so as to be displaceable in unison with the displaceable electrode unit.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional drawing of one embodiment of an actuatable capacitive transducer of the invention.

FIG. 2 is an exploded-view drawing of a multi-plate capacitor of the actuatable capacitive transducer depicted inFIG. 1.

FIG. 3 is an exploded-view drawing of the center plate of a multi-plate capacitor of the actuatable capacitive transducer depicted inFIG. 1.

FIG. 4 is a multi-plate capacitor of the actuatable capacitive transducer depicted inFIG. 1: a) fully-assembled drawing; and b) photograph of a built multi-plate capacitor showing its size relative to a US dime.

FIG. 5 is additional perspectives of the actuatable capacitive transducer depicted inFIG. 1: a) exploded-view drawing; and b) fully-assembled drawing.

FIG. 6 illustrates the major aspects of the electrical configuration of the actuatable capacitive transducer depicted inFIG. 1. Relative dimensions of the actuatable capacitive transducer are improper for the sake of clarity.

FIG. 7 is a photograph of a built nanoindentation head.

FIG. 8 is a built TEM holder: a) photograph of the holder shown in entirety; b) photograph showing the tongue portion of the holder in detail; and c) photograph showing the holder inserted into a JEOL JEM 3010 TEM.

FIG. 9 is a block diagram for a nanoindentation head's control system.

FIG. 10 is a built actuatable capacitive transducer's transient response in a JEOL JEM 3010 TEM: a) out-of-contact impulse-ring-down trace for the open-loop mode; including the exponential decay of the trace's envelope; and b) out-of-contact step-response trace while using the displacement control mode.

FIG. 11 illustrates means for bleeding charge from a conductive indenter when operating in a JEOL JEM 3010 TEM and compares quantitative in-situ TEM cantilever bending data for two electrical configurations: a) drawing of a proper electrical configuration; b) force-displacement curve while using the displacement control mode, for an improper electrical configuration; and c) force-displacement curve while using the displacement control mode, for the proper electrical configuration depicted in a).

FIG. 12 is a set of quantitative in-situ TEM nanoindentation data for nanograin aluminum obtained with a built actuatable capacitive transducer operating in a JEOL JEM 3010 TEM: a) force-displacement curve while using the displacement control mode; b) force-displacement curve while using the single-sided force-feedback control mode; and c) two video frames extracted from a recorded stream of TEM images that correlates to the force-displacement curve in a).

FIG. 13 is a set of quantitative in-situ TEM nanoindentation data for single-crystal silicon obtained with a built actuatable capacitive transducer operating in a JEOL JEM 3010 TEM: a) force-displacement curve while using the displacement control mode; and b) post-test TEM image and electron diffraction patterns.

DETAILED DESCRIPTION

In the following Detailed Description, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced. In this regard, directional terminology, such as “top,” “bottom,” “front,” “back,” “leading,” “trailing,” etc., is used with reference to the orientation of the Figure(s) being described. Because components of embodiments of the present invention can be positioned in a number of different orientations, the directional terminology is used for purposes of illustration and is in no way limiting. It is to be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present invention. The following detailed description, therefore, is not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims.

An actuatable capacitive transducer suitable for quantitative in-situ TEM nanoindentation is one novel aspect of the invention. A detailed description of one or more embodiments of an actuatable capacitive transducer according to the present invention follows.

FIG. 1 is a cross-sectional drawing of one embodiment of anactuatable capacitive transducer30 according to the present invention.Actuatable capacitive transducer30 includes an electricallyconductive transducer body32, a firstmulti-plate capacitor34, a secondmulti-plate capacitor36, and acoupling shaft46. First and secondmulti-plate capacitors34 and36 are attached toconductive transducer body32, without electrically shorting them toconductive transducer body32, such that they are maintained at a fixed separation and are substantially parallel to each other. In one embodiment,conductive transducer body32 is made of titanium.

As will be described in greater detail below with respect toFIG. 1 andFIG. 2, first and secondmulti-plate capacitors34 and36 respectively includecenter plates38 and40, and each include adisplaceable electrode42 supported from aframe43 bysprings44, where “displaceable” means displaceable relative toconductive transducer body32. Couplingshaft46, as will be described in greater detail below with respect toFIG. 1 andFIG. 2, mechanically couples thedisplaceable electrodes42 to form a mechanically-coupled displaceable electrode unit, wherein the mechanically-coupled displaceable electrode unit is displaceable as one unit relative toconductive transducer body32. In one embodiment,coupling shaft46 comprises an electrically conductive threadedrod48 encased, except at its two ends, by a tightly adhered dielectric (electrically insulating)sheath50.Dielectric sheath50 is mechanically stiff in order to suppress conductive threadedrod48, which has a high ratio of length to diameter, from flexing under the influence of a force.Dielectric sheath50 also electrically insulates conductive threadedrod48 from thedisplaceable electrodes42. In one embodiment, conductive threadedrod48 is made of brass anddielectric sheath50 is made of Macor®, a machinable ceramic.

In one embodiment, as illustrated byFIG. 1,actuatable capacitive transducer30 further includes adielectric sleeve52, adielectric standoff54, aprobe wire tab56, and an electricallyconductive nut58.Dielectric sleeve52 reinforces the connection ofcoupling shaft46 to thedisplaceable electrode42 of firstmulti-plate capacitor34.Dielectric standoff54 reinforces the connection ofcoupling shaft46 to thedisplaceable electrode42 of secondmulti-plate capacitor36 and serves as a base forprobe wire tab56.Probe wire tab56 slips over an unsheathed end of conductive threadedrod48 which is located internally toconductive transducer body32 and is retained againstdielectric standoff54 by screwing onconductive nut58, such thatprobe wire tab56 is in intimate electrical contact with conductive threadedrod48. In one embodiment,dielectric sleeve52 anddielectric standoff54 are each made of Macor®,probe wire tab56 is made of beryllium copper, andconductive nut58 is made of brass.

In one embodiment, as illustrated byFIG. 1,actuatable capacitive transducer30 includes an electricallyconductive probe60. In one embodiment,conductive probe60 includes an electricallyconductive indenter62 which is mechanically and electrically coupled to an electricallyconductive shank64.Conductive shank64 is tapped to mate with conductive threadedrod48 and includes avent hole66 to prevent a virtual leak in the high-vacuum environment of a TEM. A portion ofconductive shank64 is square in cross-section (seeFIG. 5a) for insertion into a probe mounting tool designed similarly to a nut driver. In one embodiment,conductive probe60 is screwed onto an unsheathed end of conductive threadedrod48 which is located externally toconductive transducer body32, such thatconductive probe60 is in intimate electrical contact with conductive threadedrod48. It is noted that the ability to screwconductive probe60 on and off conductive threadedrod48 facilitates probe storage or probe exchange whenever necessary. In one embodiment,conductive shank64 is made of titanium andconductive indenter62 is made of diamond highly through doped with boron and ground to a well-defined geometry, such as the Berkovich geometry, for example. A standard method of attaching a diamond indenter to a titanium shank involves vacuum brazing.

FIG. 2 is an exploded-view drawing of one embodiment of a multi-plate capacitor according to the present invention, such as firstmulti-plate capacitor34 ofFIG. 1. It is noted that the illustration ofFIG. 2 and the following description also applies to secondmulti-plate capacitor36. In addition tocenter plate38, firstmulti-plate capacitor34 includes a firstouter plate70, a secondouter plate72, which is substantially identical to firstouter plate70, a firstdielectric spacer74, and a seconddielectric spacer76, which is substantially identical to firstdielectric spacer74. In one embodiment, first and secondouter plates70 and72 each comprise a dielectric slab having astationary electrode80 in the shape of a ring patterned onto one face of the dielectric slab, aguard ring82 patterned aroundstationary electrode80, and aground plane84 patterned onto the opposite face of the dielectric slab. The term “stationary”, with regard tostationary electrode80, means stationary relative to theconductive transducer body32. In one embodiment, first and secondouter plates70 and72 are made of TMM® 4 patterned with electro-deposited copper cladding, TMM® 4 being a ceramic/polytrifluoroethylene laminate often used in outer space applications, and first and seconddielectric spacers74 and76 are made of aluminum heavily anodized to achieve electrically insulating surfaces.

First and secondouter plates70 and72, andcenter plate38 each include acenter hole86. In one embodiment,center hole86 ofcenter plate38 is smaller in diameter than center holes86 of first and secondouter plates70 and72, as indicated by the pair of vertical dashed lines inFIG. 2.

Multi-plate capacitor34 is constructed as a stack in the order of firstouter plate70, firstdielectric spacer74,center plate38, seconddielectric spacer76, and secondouter plate72. Again, it is noted that the following description applies to both first and secondmulti-plate capacitors34 and36.Stationary electrode80 of firstouter plate70 faces one face ofdisplaceable electrode42 ofcenter plate38. Stationary electrode80 (not shown inFIG. 2) of secondouter plate72 faces the opposite face ofdisplaceable electrode42 ofcenter plate38. Firstdielectric spacer74 separates and electrically insulates firstouter plate70 fromcenter plate38.Second dielectric spacer76 separates and electrically insulates secondouter plate72 fromcenter plate38. The thickness of firstdielectric spacer74 is a dominant factor in determining a first electrode gap, corresponding to the separation betweenstationary electrode80 of firstouter plate70 anddisplaceable electrode42, and the thickness of seconddielectric spacer76 is a dominant factor in determining a second electrode gap, corresponding to the separation betweenstationary electrode80 of secondouter plate72 anddisplaceable electrode42.

From a mechanical design viewpoint, first and secondmulti-plate capacitors34 and36 may differ with respect to the thickness ofdielectric spacers74 and76. In one embodiment,dielectric spacers74 and76 of the firstmulti-plate capacitor34 each have a thickness of 100 μm, anddielectric spacers74 and76 of secondmulti-plate capacitor36 each have a thickness of 75 μm. In this embodiment, the difference in thickness betweendielectric spacers74 and76 of first and secondmulti-plate capacitors34 and36 is related to firstmulti-plate capacitor34 functioning primarily as an electrostatic actuator (and secondarily as a capacitive displacement sensor), and secondmulti-plate capacitor36 functioning as a capacitive displacement sensor. It is noted that in some instances, firstmulti-plate capacitor34 is referred to as the “electrostatic actuator”, and secondmulti-plate capacitor36 is referred to as the “capacitive displacement sensor”, keeping in mind that the electrostatic actuator also functions as an additional capacitive displacement sensor in some embodiments.

FIG. 3 is an exploded-view drawing illustrating one embodiment of a center plate of a multi-plate capacitor according to the present invention, such ascenter plate38 of firstmulti-plate capacitor34. It is noted that the illustration ofFIG. 3 and the following description also applies to centerplate40 of secondmulti-plate capacitor36. In one embodiment,center plate38 includes afirst spring sheet90, asecond spring sheet92, which is substantially identical tofirst spring sheet90, and astabilizer94. In one embodiment, first andsecond spring sheets90 and92 each have aninner ring96 supported by a set of three substantially identical and equally spacedsprings98 which are coupled to anouter ring100. In one embodiment, eachspring98 includes an arc shapedfirst leg102 following the circumference ofinner ring96, aturning segment104, and an arc shapedsecond leg106 following the circumference ofouter ring100, with arc shaped first andsecond legs102 and106 being adjacent to one another. It is noted that together, springs98 of first andsecond spring sheets90 and92 are represented assprings44 inFIG. 2. First andsecond spring sheets90 and92 also include a displaceable-electrode wire tab108 extending fromouter ring100. In one embodiment, first andsecond spring sheets90 and92, andstabilizer94 are made of beryllium copper.

In one embodiment,stabilizer94 includes aninner ring110 which is initially connected to anouter ring112 by a set of three substantially identical and equally spacedtemporary connectors114. In one embodiment,inner ring110 ofstabilizer94 includes a set of six substantially identical and equally spaced weight-reduction holes116. Initially, as indicated by the vertical dashed lines inFIG. 3, aninside diameter120 ofinner ring110 ofstabilizer94 is smaller thaninside diameters122 ofinner rings96 of first andsecond spring sheets90 and92. Ultimately, theinside diameters122 ofinner rings96 of first andsecond spring sheets90 and92 and insidediameter120 ofinner ring110 ofstabilizer94 are enlarged and form a uniform final diameter forcenter hole86 ofcenter plate38, as illustrated inFIG. 2.

Center plate38 is constructed as a stack in the order offirst spring sheet90,stabilizer94, andsecond spring sheet92. In one embodiment,inner rings96 of first andsecond spring sheets90 and92 andinner ring110 ofstabilizer94 are laminated together to formdisplaceable electrode42. Similarly,outer rings100 of first andsecond spring sheets90 and92 andouter ring112 ofstabilizer94 are laminated together to formframe43. It is noted that springs98 of first andsecond spring sheets90 and92 must be kept free of adhesive and form springs44. Displaceable-electrode wire tabs108 of first andsecond spring sheets90 and92 are wired together to ensure that first andsecond spring sheets90 and92 are at the same electrical potential. In one embodiment, as a precaution against introducing a virtual leak in the high-vacuum environment of a TEM, weight-reduction holes116 ofstabilizer94 are filled with adhesive during the process of constructingcenter plate38.

In some instances, construction ofcenter plate38, as described above, results in a non-concentric alignment of theinside diameters122 ofinner rings96 of first andsecond spring sheets90 and92 and insidediameter120 ofstabilizer94. In one embodiment, using the smallerinside diameter120 ofinner ring110 ofstabilizer94 as a pilot hole, insidediameters122 ofinner rings96 of first andsecond spring sheets90 and92 andinner diameter120 ofstabilizer94 are enlarged by drilling to establish a substantially uniform final diameter ofcenter hole86 ofcenter plate38. After completing the drilling operation,temporary connectors114 are removed which freesdisplaceable electrode42 to move as one unit relative to frame43 when influenced by a force. The multilayer design of thecenter plate38 enablessprings44 to have a low spring constant simultaneous withdisplaceable electrode42 having high flexural rigidity.

In one embodiment, the spring constant ofsprings44 is optimized relative to the flexural rigidity ofdisplaceable electrode42. In one embodiment, the spring constant ofsprings44 was optimized with the aid of modeling by finite-element analysis (FEA). In one embodiment, the finalized design ofsprings44 resulted in a nominal modeled spring constant of 197N/m for actuatable capacitive transducer30 (each of twelve springs contributing 16.4N/m). Taking into account dimensional tolerances, spring constant k of actuatable capacitive transducer30 is predicted to fall in the range of 111-345N/m, primarily as a consequence of a strong dependence on an uncertainty in a thickness t of the first andsecond spring sheets90 and92 (k∝t³). In one embodiment, actuatablecapacitive transducer30 was determined to have a measured k of 259N/m, somewhat higher than a nominal modeled k of 197N/m, but within a range of possible values. It is noted that the nominal modeled k is approximately the same as that of Hysitron's three-plate capacitive transducer, which is comprised of a single three-plate capacitor of square shape having a total of eight springs of different shape and dimensions in comparison tosprings44 of actuatable capacitivetransducer30.

In one embodiment, FEA was used further to predict whethersprings44 obeyed Hooke's law whendisplaceable electrode42 was forced to displace up to 5 μm from its natural state in a manner that only caused a uniform change in the electrode gaps, wherein “natural state” refers to a positional state ofdisplaceable electrode42 when not under the influence of electrostatic and indenter-sample forces. The FEA results predict excellent adherence to Hooke's law over this range of displacement, a range easily large enough for quantitative in-situ TEM nanoindentation because the depth of electron transparency in a sample is only in the vicinity of 300 nm for a 300 kV electron beam. FEA was used further still to predict the largest local strain induced insprings44 whendisplaceable electrode42 was forced to displace 75 μm from its natural state in the manner described above. This amount of displacement is equivalent todisplaceable electrode42 of the more narrowly gapped secondmulti-plate capacitor36, in one embodiment, being forced to contact a neighboring stationary electrode. At 75 μm displacement, the largest local strain insprings44 is predicted to be 0.08%, well under the expected elastic strain limit of 0.2%.

Returning toFIG. 2,multi-plate capacitor34 is formed by adhering firstdielectric spacer74 both to firstouter plate70 andframe43 ofcenter plate38, and by adhering seconddielectric spacer76 both to secondouter plate72 andframe43 ofcenter plate38.Springs44 anddisplaceable electrode42 must be kept free of adhesive during the joining procedure.

FIG. 4A is a perspective view representative of one embodiment ofmulti-plate capacitor34 in an assembled condition. As can be seen inFIG. 4B, assembledmulti-plate capacitor34 is substantially smaller than a U.S. dime.

FIG. 5A is an exploded-view drawing further illustrating actuatable capacitivetransducer30 described byFIGS. 1 through 4A above.FIG. 5B is a perspective view drawing illustrating actuatable capacitivetransducer30 in an assembled condition. With respect toFIG. 5A,dielectric sheath50 ofcoupling shaft46 has asegment130 of a major diameter and first andsecond segments132 and134 of a minor diameter, with minor-diameter segment132 being longer than minor-diameter segment134. The minor diameter of first andsecond segment132 and134 is a tight fit to the drilled-out uniform final diameter of center holes86 ofcenter plates38 and40 of first and secondmulti-plate capacitors34 and36. The major diameter ofsegment130 is larger than the minor diameter of first andsecond segments132 and134, but is small enough in comparison to the diameter of center holes86 of first and secondouter plates70 and72 of first and secondmulti-plate capacitors34 and36 to preventcoupling shaft46 from contacting the relevant outer plates after assembly of actuatablecapacitive transducer30.

With reference toFIG. 5A, the following describes an example of a sequence of steps for assemblingactuatable capacitive transducer30. First, pre-assembled firstmulti-plate capacitor34 is slipped over longer minor-diameter segment132 ofdielectric sheath50, which is pre-adhered to conductive threadedrod48.Displaceable electrode42 of firstmulti-plate capacitor34 is then adhered against a shoulder defined by the transition from longer minor-diameter segment132 to major-diameter segment130 ofdielectric sheath50. Next,dielectric sleeve52 is slipped over longer minor-diameter segment132 ofdielectric sheath50.Dielectric sleeve52 is then adhered todisplaceable electrode42 of firstmulti-plate capacitor34 and todielectric sheath50, such thatdielectric sleeve52 does not contact the outer plate through which it passes. Next, pre-assembled secondmulti-plate capacitor36 is slipped over shorter minor-diameter segment134 ofdielectric sheath50.Displaceable electrode42 of secondmulti-plate capacitor36 is then adhered against a shoulder defined by the transition from shorter minor-diameter segment134 to major-diameter segment130 ofdielectric sheath50. Next,dielectric standoff54 is slipped over the unsheathed end of conductive threadedrod48 now protruding from secondmulti-plate capacitor36.Dielectric standoff54 is then adhered to conductive threadedrod48 and todisplaceable electrode42 of secondmulti-plate capacitor36, such thatdielectric standoff54 does not contact the outer plate through which it passes. Next,probe wire tab56 is slipped over the unsheathed end of conductive threadedrod48 now protruding fromdielectric standoff54, and is retained by screwing onconductive nut58. Screwingconductive probe60 onto the remaining unsheathed end of conductive threadedrod48 is delayed until just prior to use in order to diminish the likelihood of inadvertently damagingconductive indenter62.

With reference toFIG. 5B,conductive transducer body32 has a first set ofports140 and a second set ofports142 to facilitate attaching the now mechanically-coupled first and secondmulti-plate capacitors34 and36 toconductive transducer body32. It is noted that not all ports of first and second sets ofports140 and142 are visible in the illustration ofFIG. 5B.Conductive transducer body32 also includescutouts144 which will be described in greater detail below.

Continuing with the example sequence of steps for assemblingactuatable capacitive transducer30 described above, the now mechanically-coupled first and secondmulti-plate capacitors34 and36 are inserted intoconductive transducer body32 such that firstmulti-plate capacitor34 is aligned with first set ofports140 and secondmulti-plate capacitor36 is approximately aligned with second set ofports142. Next, adhesive is injected into first set ofports140 to fix firstmulti-plate capacitor34 toconductive transducer body32.

Optimum attachment of secondmulti-plate capacitor36 toconductive transducer body32 requires finely manipulating the position of secondmulti-plate capacitor36 until each or a specific one of thedisplaceable electrodes42 of first and secondmulti-plate capacitors34 and36 resides, as close as possible, midway between the corresponding flanking stationary electrodes80 (seeFIG. 2). After achieving the desired condition, adhesive is injected into second set ofports142 to fix secondmulti-plate capacitor36 toconductive transducer body32. In one embodiment, the method used to maintain the desired distance between first and secondmulti-plate capacitors34 and36 during adhesive curing resulted in only a 90 nm deviation from perfectly balancing the gaps of first multi-plate capacitor34 (the electrostatic actuator). One particular nanoindentation operating mode requireselectrostatic actuator34 having well-balanced electrode gaps.

Properly fixing the position of secondmulti-plate capacitor36 requires this assembly step be done withcoupling shaft46 horizontal in order to match the eventual orientation of actuatable capacitive transducer30 in a TEM. If this assembly step is done withcoupling shaft46 aligned with gravity for example,displaceable electrodes42 of first and secondmulti-plate capacitors34 and36 would end up far from midway between the flankingstationary electrodes80 upon reorientingactuatable capacitive transducer30 for insertion into a TEM.

In one embodiment, as can be seen inFIG. 5A, actuatable capacitive transducer30 has acentral axis148 about which its components are predominantly circular in shape, and about which its components are predominantly concentric. The choice of circular shapes, rather than square shapes for example, is motivated by actuatablecapacitive transducer30 being configured to be housed in a TEM holder. TEM holders, sometimes referred to as TEM rods, typically posses a tubular geometry. By choosing circular shapes, the electrode areas can be maximized. Also regarding electrode areas,displaceable electrodes42 have a smaller inside diameter and a larger outside diameter in comparison tostationary electrodes80. This intentional mismatch in diameters suppresses a change in overlapping electrode area in theevent displaceable electrodes42 are forced to shift sideways with respect to thestationary electrodes80.

As described above, actuatable capacitive transducer30 must be oriented withcoupling shaft46 horizontal when operating in a TEM. A horizontal orientation enablesconductive indenter62 to intersect the vertically-aligned electron beam of a TEM. As a consequence of this horizontal orientation,conductive probe60 will tilt substantially downward if the tilting moment owing to gravity acting on the mass fromconductive indenter62 todisplaceable electrode42 of firstmulti-plate capacitor34 is not countered by some means. In addition,conductive indenter62 contacting a sample having its surface slanted relative tocentral axis148 of actuatablecapacitive transducer30 will cause a net sideways force, thereby introducing an additional tilting moment. On account of TEM design, the distance fromconductive indenter62 todisplaceable electrode42 of firstmulti-plate capacitor34 cannot be significantly shortened to substantially reduce these tilting moments.

Countering tilting moments is a major impetus for employing secondmulti-plate capacitor36. By separating the first and secondmulti-plate capacitors34 and36 by a significant fraction of the distance fromconductive indenter62 todisplaceable electrode42 of firstmulti-plate capacitor34, the tendency to tilt is greatly reduced. However, there is a compromise between lengthening the portion ofcoupling shaft46 betweendisplaceable electrodes42 of the first and secondmulti-plate capacitors34 and36 and preserving a high mechanical natural frequency, because the mass ofcoupling shaft46 is the dominant mass carried by thesprings44.

The following Expression E.1 can be used to calculate the mechanical natural frequency v_oof a spring-mass system:

$\begin{array}{cc}{v}_o=\frac{1}{2\pi }\sqrt{\frac{k}{m}};& E\mathrm{.1}\end{array}$
where k retains the meaning defined above and m is the sprung mass of actuatablecapacitive transducer30. In one embodiment of actuatablecapacitive transducer30, v_owas measured to be 133 Hz withconductive probe60 attached, which yielded 372 mg for m given the measured k of 259N/m. The measured v_oof actuatable capacitive transducer30 is comparable to what generally is found for Hysitron's three-plate capacitive transducer equipped with its probe, which is not electrically conductive.

FIG. 6 is a diagram illustrating aspects of the electrical configuration of actuatablecapacitive transducer30. As illustrated byFIG. 6, the electrostatic actuator (i.e., first multi-plate capacitor34) has a different electrical configuration compared to the capacitive displacement sensor (i.e., second multi-plate capacitor36). Signals inputted toelectrostatic actuator34 include V₁+V_m, as indicated at150, to the one ofstationary electrodes80 ofelectrostatic actuator34 closest toconductive indenter62, and V₂−V_m, as indicated at152, to the otherstationary electrode80 of theelectrostatic actuator34. Signals inputted to the capacitive displacement sensor include +V_mto the capacitive displacement sensor's stationary electrode closest to the conductive indenter and −V_mto the other stationary electrode of the capacitive displacement sensor.

Input signals V₁and V₂are electrostatic actuation voltages, while input signals +V_mand −V_m, indicated at154 and156, are high-frequency modulation voltages equal in frequency, waveform, and amplitude but different in phase by 180°. The frequency of +V_mand −V_mis much higher than v_o; therefore, actuatablecapacitive transducer30 does not mechanically respond to these input signals. In one embodiment of a built actuatable capacitive transducer30, both +V_mand −V_mare 130 kHz square waves with an amplitude of 10V peak-to-peak, and both V₁and V₂cover the range of 0-600V.Displaceable electrode42 ofelectrostatic actuator34 is effectively at ground relative to V₁and V₂.

Electrostatic actuator34 outputs a V_out1signal, as indicated at158, from correspondingdisplaceable electrode42.Capacitive displacement sensor36 outputs a V_out2signal, as indicated at160, from correspondingdisplaceable electrode42. The frequency and the waveform of +V_mand −V_mdictate the frequency and the waveform ofV_out1158 andV_out2160. In a fashion similar to Hysitron's three-plate capacitive transducer and to the IFM sensor, bothelectrostatic actuator34 andcapacitive displacement sensor36 are electrically configured to execute the well-established differential capacitance half-bridge method of displacement detection.

With the differential capacitance half-bridge method, an output signal V_outof an appropriately configured multi-plate capacitor (specifically an appropriately configured three-plate capacitor) is ideally given by the following Expression E.2:

$\begin{array}{cc}{v}_{\mathrm{out}}=\frac{C_1-C_2}{{\mathrm{<figure-callout\; label="C"\; filenames="US08453498-20130604-D00006.png,US08453498-20130604-D00011.png"\; state="\{\{state\}\}">C</figure-callout>}}_1+{\mathrm{<figure-callout\; label="C"\; filenames="US08453498-20130604-D00006.png"\; state="\{\{state\}\}">C</figure-callout>}}_2}V_m;& E\mathrm{.2}\end{array}$
where C₁is the capacitance betweendisplaceable electrode42 and one neighboringstationary electrode80, C₂is the capacitance betweendisplaceable electrode42 and the other neighboringstationary electrode80, and |V_m| is the amplitude of either +V_mor −V_m. Output signal V_outcan be of either sign depending on which of C₁and C₂is larger. The amplitude of V_outis zero when C₁=C₂, and is |V_m| whendisplaceable electrode42 is in contact with either neighboringstationary electrode80. Expression E.2 applies both to V_out1and V_out2. The differential capacitance half-bridge method has the characteristic of being relatively insensitive to tilting ofdisplaceable electrodes42 relative tostationary electrodes80 and, thus, to vibrations that induce oscillatory tilting. This is particularly important, becauseactuatable capacitive transducer30 is most susceptible to vibrations that induce oscillatory tilting on account of its horizontal orientation in a TEM.

In terms of geometric parameters, the capacitance C of a parallel-plate capacitor is given by Expression E.3 below:

$\begin{array}{cc}C=\frac{{\varepsilon }_{o}A}{d};& E\mathrm{.3}\end{array}$
where ∈_ois the electrical permittivity constant (8.85×10⁻¹²F/m), A is the overlapping electrode area, and d is the electrode gap. Expression E.3 can be used to calculate either multi-plate capacitor's nominal capacitance, i.e., the value of C₁or C₂for the state in which C₁=C₂which ideally corresponds to balanced electrode gaps. In one embodiment, the nominal capacitance ofelectrostatic actuator34 is calculated to be 0.80 pF, assuming d′₁=d′₂=100 μm and A=9.03 mm², where d′₁and d′₂are electrodegaps162 and164 ofelectrostatic actuator34. In one embodiment, the nominal capacitance ofcapacitive displacement sensor36 is calculated to be 1.1 pF, assuming d₁=d₂=75 μm and A=9.03 mm², where d₁and d₂areelectrode gaps166 and168 ofcapacitive displacement sensor36. In one embodiment, actuatablecapacitive transducer30 is designed such that A is single valued. A nominal capacitance of 1 pF is the rule-of-thumb cutoff for good design practice; therefore, actuatablecapacitive transducer30 is configured to be in the vicinity of the rule-of-thumb cutoff.

Replacing C₁and C₂in E.2 with

$\frac{{\varepsilon }_{o}A}{{\mathrm{<figure-callout\; label="d"\; filenames="US08453498-20130604-D00006.png,US08453498-20130604-D00011.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}\mathrm{and}\frac{{\varepsilon }_{o}A}{{\mathrm{<figure-callout\; label="d"\; filenames="US08453498-20130604-D00006.png"\; state="\{\{state\}\}">d</figure-callout>}}_2},$
respectively, results in the following Expression E.4 for capacitive displacement sensor36:

$\begin{array}{cc}{V}_{\mathrm{out}2}=\frac{d_2-d_1}{{\mathrm{<figure-callout\; label="d"\; filenames="US08453498-20130604-D00006.png"\; state="\{\{state\}\}">d</figure-callout>}}_2+{\mathrm{<figure-callout\; label="d"\; filenames="US08453498-20130604-D00006.png,US08453498-20130604-D00011.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}V_m=\frac{\Delta d}{\stackrel{\_}{d}}V_m;& E\mathrm{.4}\end{array}$
whered is the constant mean of d₁and d₂, and where Δd (which can be of either sign) is the change in one electrode gap (e.g., the change in d₂) relative to the condition in which the electrode gaps are balanced (d₁=d₂=d). The change in the other electrode gap (e.g., the change in d₁) relative to the balanced condition is identical in magnitude but opposite in sign. A smalld is conducive to high displacement sensitivity, which is the reason, in one embodiment, for utilizing thinnerdielectric spacers74 and76 forcapacitive displacement sensor36 relative toelectrostatic actuator34. Expression E.4 predicts V_out2to be a perfectly linear function of Δd over the entire range of displacement. But in practice, parasitic capacitance not dependent on

$\frac{\Delta d}{\stackrel{\_}{d}}$
restricts satisfactory linearity to some range less than the full range about the balanced condition. In one embodiment, both first and secondmulti-plate capacitors34 and36 of actuatable capacitive transducer30 (an equation analogous to E.4 is applicable to the displacement sensing function of electrostatic actuator34) are satisfactorily linear over a displacement range of ±5 μm about the natural state ofdisplaceable electrodes42. Larger displacements have not been experimentally investigated as they are not necessary for quantitative in-situ TEM nanoindentation.

Focusing now on electrostatic actuation, the electrostatic force F_egenerated by a parallel-plate capacitor comprised of a displaceable electrode and a stationary electrode is given by the following Expression E.5:

$\begin{array}{cc}{F}_e=\frac{{\kappa }_o}{\left(1-\delta /d_o\right)}{\mathrm{<figure-callout\; label="V"\; filenames="US08453498-20130604-D00006.png"\; state="\{\{state\}\}">V</figure-callout>}}^2;& E\mathrm{.5}\end{array}$
where V is the electrostatic actuation voltage across the two electrodes, d_ois the electrode gap when V=0, δ is the displaceable electrode displacement from d_o, and where the electrostatic force constant κ_ois given by Expression E.6 below:

$\begin{array}{cc}{\kappa }_o=\frac{{\varepsilon }_{o}A}{2d_{\mathrm{<figure-callout\; label="o"\; filenames="US08453498-20130604-D00006.png"\; state="\{\{state\}\}">o</figure-callout>}}^2};& E\mathrm{.6}\end{array}$
where ∈_oand A retain their previously expressed definitions. In general, δ can be of either sign depending on the nature of the force displacing the displaceable electrode; however, F_ecan only cause the displaceable electrode to be attracted to the stationary electrode on account of its V²dependence.

Assume V in E.5 corresponds to V₁and that V₂=0. Also assume thatconductive probe60 is sufficiently blocked from moving so that δ=0 always. Setting d_oequal to a chosen 100 μm thickness ofdielectric spacers74 and76 ofelectrostatic actuator34 results in actuatablecapacitive transducer30 having an expected κ_oof 4.0 nN/V²and an expected maximum blocked F_eof 1.4 mN at V₁'s maximum of 600V. In one embodiment, the electrostatic force constant κ_oand the maximum blocked F_eof a built actuatable capacitive transducer30 were determined to be 3.6 nN/V²and 1.3 mN, respectively, both reasonably close to expectation. The capacity to generate a maximum blocked F_ein the vicinity of 1 mN is a good compromise between achieving high resolution in F_eand generating enough F_eto indent a wide variety of samples up to their maximum depth of electron transparency, which is the reason for utilizing thickerdielectric spacers74 and76 forelectrostatic actuator34 relative to capacitivedisplacement sensor36 in one embodiment.

In reality, δ is permitted to change. Displacement ofdisplaceable electrode42 must be assumed to be increasingly positive whenconductive probe60 moves toward a sample in order to be compatible with expression E.5 above. A changing δ affects the scaling between F_eand V²through the denominator of expression E.5, the scaling being increasingly enhanced when δ becomes increasingly positive and being increasingly diminished when δ becomes increasingly negative. In most instances, V₂remains at zero while V₁is being varied during the nanoindentation test, but V₂being connected provides a benefit nonetheless. Often, the dominant contributor of noise to V₁and V₂is found to be in-phase AC line noise; therefore, the electrostatic force noise associated with AC line noise present on V₂tends to cancel the electrostatic force noise associated with AC line noise of the same phase present on V₁.

Still assuming V₂=0, F_erepresents a total applied force (always positive if non-zero) equal to the contact force F_e(positive if repulsive to adhere to convention) plus the spring force F_s=kδ (the customary minus sign is dropped for convenience), which is a consequence of the parallel loading configuration. Hence, the following Expression E.7 can be used to calculate the contact force:
F_c=F_e−kδ  E.7.
Expression E.7 also applies to actuation withconductive indenter62 far from a sample. In that case, F_c=0 and F_e=kδ.

The snap-to-contact instability and the spark-gap instability must be kept in mind when actuating electrostatically. To simplify the following discussion, again assume V₂=0. The snap-to-contact instability refers todisplaceable electrodes42 suddenly snapping toward the electrostatic actuator'sstationary electrode80 with V₁applied. The possibility of this happening can be deduced from electrostatic force gradient vs. spring constant considerations, and is predicted to occur when d₁narrows to ⅔d_o(or equivalently when δ=⅓d_o) if the resistance to motion obeys Hooke's law; a higher order resistance to motion retards this instability. The spark-gap instability refers to a spark crossing d₁when the electric field strength given by the ratio of V₁to d₁exceeds a critical value, which has the highest likelihood when the snap-to-contact instability is reached, but which can happen even prior to reaching the snap-to-contact instability. The critical electric field strength depends on pressure and has the lowest value in the corona discharge region in the vicinity of 10⁻²-10⁻³torr; therefore, actuatable capacitive transducer30 should not be actuated while pumping down to the ˜10⁻⁷torr operating pressure of a TEM. Fortunately, the spark-gap instability is of much reduced concern at ˜10⁻⁷torr. The instrument's software limits δ to 5 μm to ensure the snap-to-contact instability and the spark-gap instability never occurring.

Drive cards ordinarily used for Hysitron's three-plate capacitive transducers facilitate the electrical configurations of the first and secondmulti-plate capacitors34 and36 of actuatable capacitivetransducer30 and the following describes their employment in one embodiment.Electrostatic actuator34 is electrically connected to a first drive card andcapacitive displacement sensor36 is electrically connected to a second drive card, the first and second drive cards being identical in design but different in implementation. Each of the first and second drive cards (one can be seen in the photograph ofFIG. 4B) generates +V_mand −V_mand has the capacity for coupling electrostatic actuation voltages to these high-frequency modulation signals. The first drive card forelectrostatic actuator34 couples V₁and V₂supplied by a transducer controller to +V_mand −V_mgenerated by this drive card in the manner described above. The second drive card forcapacitive displacement sensor36 simply couples a ground signal supplied by the transducer controller to +V_mand −V_mgenerated by this drive card to disable electrostatic actuation.

Each of the first and second drive cards has a preamplifier having high input impedance and low output impedance. Each of the first and second drive cards also has circuitry for synchronous demodulation of the preamplifier's output as well as circuitry for subsequent low-pass filtering of the synchronous demodulator's output to generate a useful displacement signal. The first drive card's preamplifier receives V_out1fromelectrostatic actuator34. The second drive card's preamplifier receives V_out2fromcapacitive displacement sensor36. The first drive card ultimately outputs V_disp1to the transducer controller for amplification and filtering beyond what is provided by this drive card, V_disp1being its useful displacement signal. The second drive card ultimately outputs V_disp2to the transducer controller for amplification and filtering beyond what is provided by this drive card, V_disp2being its useful displacement signal. In general, V_disp1≠V_disp2but both represent δ if properly calibrated, e.g., via measurement of V_disp1and V_disp2vs. the displacement readout of an interferometer. In one embodiment, invoking a single modulation frequency of 130 kHz did not cause detectable coupling between V_disp1and V_disp2. Separating the modulation frequency of the first drive card from that of the second drive card by several times the roll-off frequency of the post-demodulation low-pass filters can be employed to suppress coupling between V_disp1and V_disp2if problematic.

Points available on first and secondmulti-plate capacitors34 and36 for wire soldering are illustrated inFIG. 4A. Wires from the drive cards that carry the signals to be inputted tostationary electrodes80 are soldered to stationary-electrode wire pads170. Wires to the drive cards that carry the signals being outputted bydisplaceable electrodes42 are soldered to displaceable-electrode wire tabs108. Wires from the drive cards that carry the ground signal are soldered to the ground planes84 of first and secondmulti-plate capacitors34 and36 and also to theconductive transducer body32; these grounded elements serve as electrical shields. Wires from the drive cards that carry guard signals are soldered to guard-ring wire pads172 (seeFIG. 4A). The guard signal ofelectrostatic actuator34 corresponds to the output of the first drive card's preamplifier, with both guard rings82 ofelectrostatic actuator34 receiving this guard signal. The guard signal ofcapacitive displacement sensor36 corresponds to the output of the second drive card's preamplifier, with both guard rings82 ofcapacitive displacement sensor36 receiving this guard signal. The purpose is to guard the easily loaded signals present ondisplaceable electrodes42. Perimeter holes174, as shown inFIG. 4A facilitate wire routing.Cutouts144 inconductive transducer body32, as illustrated inFIG. 5B provide access to the soldering points after assembly of actuatablecapacitive transducer30, and also serve as venting for the purpose of evacuating air in a TEM.

Ordinarily, it is desirable to position the drive cards in very close proximity to the corresponding one of the first and secondmulti-plate capacitors34 and36 to minimize the length of wiring carrying the easily loaded signals being outputted bydisplaceable electrodes42. However, placing the drive cards in high vacuum raises considerable thermal management and outgassing load issues. Consequently, the drive cards reside in the posterior of the TEM holder that remains at atmospheric pressure and results in a distance of approximately 1 ft between the drive cards andactuatable capacitive transducer30 located at the anterior of the TEM holder Vacuum-compatible electrical feedthroughs facilitate the passage of wiring from atmospheric pressure into high vacuum. In spite of long wiring runs, actuatable capacitive transducer30 performs well in a TEM through use of cabling having minimal capacitance between its conductors and its grounded shield. Moreover, the drive cards and the cabling are held such that they move with actuatablecapacitive transducer30 whenever actuatable capacitivetransducer30 is translated relative to the TEM holder. This avoids a change in electrical layout that might change the amount of capacitance between the conductors and the grounded shield of the cabling. Guarding rather than shielding the conductors carrying the signals being outputted bydisplaceable electrodes42 has not been examined since guarding complicates the design of the cabling.

All materials associated with theactuatable capacitive transducer30, including the adhesives (specialty epoxies), the materials of the cabling (copper, Teflon®, and brass), and the solder (silver), are sufficiently low in outgassing rate to be compatible with high vacuum. Furthermore, these materials are sufficiently low in ferromagnetic content to not cause undue difficulty when subjected to a strong magnetic field. Compatibility with these aspects of a TEM also means materials compatibility with a scanning electron microscope (SEM) for quantitative in-situ SEM nanoindentation. Although not yet verified, the built actuatable capacitive transducer is potentially compatible with use in ultra-high vacuum. Obviously, the materials of the built actuatable capacitive transducer are compatible with use in air or inert gas environments as well.

FIG. 7 is a photograph illustrating one embodiment of ananoindentation head180 according to the invention. As illustrated inFIG. 7, ananoindentation head180 comprises actuatablecapacitive transducer30 mechanically coupled to a3D piezoelectric actuator182. The3D piezoelectric actuator182 includes a one-piece piezoelectric (piezo)tube184 comprised of anx-y segment186 anda z segment188; and has a hollow interior that serves as a conduit for the wiring to actuatablecapacitive transducer30. Thez segment188 is defined by an outer electrode (denoted z_outer) and an inner electrode (denoted z_inner) sandwiching the piezoelectric material. Thex-y segment186 is defined by four outer electrodes (denoted +x_outer, −x_outer, +y_outer, and −y_outer) and four inner electrodes (denoted +x_inner, −x_inner, +y_inner, and −y_inner) sandwiching the piezoelectric material. Voltages applied differentially to z_outerand z_innerwill inducez segment188 to extend or contract, thereby displacingactuatable capacitive transducer30 alongz axis190 depicted inFIG. 7. A voltage applied to +x_outerand −x_innerand a voltage of the same magnitude but of opposite polarity applied to −x_outerand +x_innerwill inducex-y segment186 to bend, thereby displacingactuatable capacitive transducer30 principally along the x axis, which is orthogonal to thez axis190. Displacing actuatable capacitivetransducer30 principally along the y axis, which is orthogonal to the x and z axes involves an analogous application of voltages to the y electrodes.

In one embodiment,3D piezoelectric actuator182 ofnanoindentation head180 is made of a hard lead zirconate titanate (PZT) ceramic, where “hard” refers to a small d₃₁piezoelectric constant, and its electrodes are of silver rather than of customary nickel to avoid nickel's ferromagnetism. Driven by a piezo controller capable of outputting differential voltages ranging from +370V to −370V,3D piezoelectric actuator182 ofnanoindentation head180 is capable of displacing actuatable capacitive transducer30 ±55 μm along the x and y axes and ±4.7 μm along thez axis190. The3D piezoelectric actuator182 is employed primarily as a sub-nm-resolution positioner, but it also participates in certain nanoindentation operating modes, and it can be used to raster scan theconductive indenter62 to image a sample's surface in the manner of an AFM if desired. Although3D piezoelectric actuator182 currently does not employ a displacement sensor dedicated to measuring the extension or the contraction ofz segment188, the choice of a hard PZT ceramic helps to improve the reliability of correlating the motion provided to the differential voltage applied.

Nanoindentation head180 is designed to be housed in a newly-developed TEM holder based largely on earlier TEM holders developed at National Center for Electron Microscopy/Lawrence Berkeley National Laboratory (NCEM/LBNL) for qualitative and semi-quantitative in-situ TEM nanoindentation (see References 6-11 and 13-17). Nevertheless, a TEM holder according to the present invention, as will be described in greater detail below, substantially outperforms these prior-art in-situ TEM nanoindentation holders, particularly with respect to load frame stiffness and coarse positioning stability, the latter aspect being related to the former aspect. In fact,Reference 10 and the erroneously titled Reference 9 pertain to taking advantage of poor load frame stiffness to deduce the contact force.

FIG. 8A is a photograph illustrating one embodiment of aTEM holder200 according to the present invention.FIG. 8B is a photograph illustrating atongue portion202 ofTEM holder200.FIG. 8C is a photograph illustratingTEM holder200 inserted into aTEM203 with its posterior204 visible. It is noted thatTEM203 illustrated inFIG. 8C comprises a JEOL JEM 3010 TEM. With reference toFIG. 7,nanoindentation head180 includes aninternal tube206 which mechanically supportsnanoindentation head180.Internal tube206 is internal to anexternal tube208, which is illustrated inFIG. 8A. Also illustrated inFIG. 8A are three coarse positioning screws210. Manually turning the three coarse positioning screws210 causes theinternal tube206 to be positioned three dimensionally with respect toexternal tube208, thereby causing thenanoindentation head180 to be positioned three dimensionally with respect totongue202, which is most easily seen inFIG. 8B. In one embodiment, the resolution of coarse positioning is 200 μm/rev. In one embodiment, as illustrated byFIG. 8B,tongue202 includes asample clamp212 to tightly hold a wedge-shaped sample, such as the one depicted inFIG. 11A below and illustrated as being indented byconductive indenter62.Sample clamp212 is easily detached fromTEM holder200 to facilitate screwing ofconductive probe60 on or off the portion of conductive threadedrod48 protruding fromcoupling shaft46 of actuatable capacitivetransducer30.Tongue202 is the portion ofTEM holder200 that inserts into the narrow pole piece gap of a TEM. Allobjects penetrating tongue202 must be confined to the dimensions of the tongue.

It is desirable to keep the sample stationary, especially when invoking nanoindentation operating modes involving3D piezoelectric actuator182 to affect the indenter-sample separation. Keeping the sample stationary enables the sample's region of interest to fully fill the TEM's field of view and eliminates the possibility of a portion of the sample's region of interest shifting out of the TEM's field of view during nanoindentation tests involving3D piezoelectric actuator182. In contrast, Nanofactory's instrument keeps its miniature two-plate capacitive transducer stationary while actuating its piezoelectric actuator carrying the sample to affect the indenter-sample separation (see Reference 20).

FIG. 9 is a block diagram illustrating generally one embodiment of acontrol system220 fornanoindentation head180 according to the present invention.Control system220 is comprised of a transducer controller222 (as mentioned above), a piezo controller224 (as mentioned above), a digital signal processor (DSP) basedcontroller226 capable of 100 million instructions per second, and acomputer228 running the instrument's software.Computer228 is in communication withDSP controller226 via a universal serial bus (USB)link230. In one embodiment,computer228 comprises a laptop computer.DSP controller226 is in communication withtransducer controller222, which is cabled, as indicated at232, to the drive cards of actuatable capacitive transducer30 housed within theTEM holder200, and withpiezo controller224, which is cabled, as indicated at234, to3D piezoelectric actuator182 also housed withinTEM holder200. In one embodiment,transducer controller222 andpiezo controller224 are based, in part, on units currently supplied with Hysitron's suite of nanoindenters. As a result,control system220 is an enabler of imaging in the manner of an AFM in addition to being an enabler of nanoindentation tests.DSP controller226, on the other hand, is an entirely new development.

DSP controller226 is programmable and has amemory space236 for storing instructions received fromcomputer228, and a memory space238 for storing digitized data to be received bycomputer228.DSP controller226 also includes a plurality of 16-bit digital-to-analog converters (DACs)240, a plurality of 16-bit analog-to-digital converters (ADCs)242, a plurality of programmable gain amplifiers (PGAs)244, a plurality of voltage attenuators (VAs)246, and a plurality of digital input-output channels (DIOs)248 to carry out its various programmed tasks.DACs240 generate analog voltages which are amplified byPGAs244. The outputs of the PGAs are further amplified either bytransducer controller222 to generate V₁and V₂to actuatablecapacitive transducer30 via the first drive card or bypiezo controller224 to generate the voltages to3D piezoelectric actuator182.ADCs242 digitize analog voltages outputted by VAs246, which receive certain analog signals to attenuate before digitization, including V_disp1and V_disp2as provided bytransducer controller222. The necessity ofPGAs244 andVAs246 is linked to a mismatch inDAC240 andADC242 saturation levels in comparison totransducer controller222 andpiezo controller224 saturation levels.DIOs248 are used to control chip states of various chips included intransducer controller222,piezo controller224, andDSP controller226.DSP controller226 generally executes control loops at a 22 kHz loop rate but can execute control loops at loop rates as high as 80 kHz. Several control loops provide the characteristic of active damping, a particularly important characteristic to provide when actuatable capacitivetransducer30 is operating in the extremely low damping environment of a TEM.

DSP controller226 enables a variety of nanoindentation operating modes which represent methods of conducting quantitative in-situ TEM nanoindentation providing that a stream of TEM images that show how the sample deforms while being indented is viewed/recorded. The following is a list of at least six nanoindentation operating modes capable of being performed by control system220:

• • 1. Load control mode—utilize either a feedback control algorithm (e.g., proportional-integral-derivative or PID) or a feedforward augmented feedback control algorithm with optionally adaptive characteristics to adjust V₁(V₂=0) in a manner that causes the contact force to meet a predetermined contact force vs. time function while keeping3D piezoelectric actuator182 static. The development of this mode for Hysitron's three-plate capacitive transducer has been described in Reference 4.
  • 2. Displacement control mode—utilize either a feedback control algorithm or a feedforward augmented feedback control algorithm with optionally adaptive characteristics to adjust V₁(V₂=0) in a manner that causes the indenter displacement to meet a predetermined indenter displacement vs. time function while keeping3D piezoelectric actuator182 static. The development of this mode for Hysitron's three-plate capacitive transducer also has been described in Reference 4.
  • 3. Single-sided force-feedback control mode (another form of displacement control)—conduct single-sided force-feedback control involving fed-back adjustments to V₁(V₂=0) while varying the differential voltage to thez segment188 of3D piezoelectric actuator182 to affect the indenter-sample separation. This mode is analogous to the torque balance operation of the IFM in the sense thatdisplaceable electrodes42 are suppressed from deflecting.
  • 4. Double-sided force-feedback control mode (vet another form of displacement control)—conduct double-sided force-feedback control involving coordinated fed-back adjustments to V₁and V₂while varying the differential voltage to thez segment188 of3D piezoelectric actuator182 to affect the indenter-sample separation. This mode also is analogous to the torque balance operation of the IFM in the sense just mentioned. However, this mode in conjunction with actuatablecapacitive transducer30 has a certain novel advantage over the torque balance operation of the IFM, which will be explained in greater detail below.
  • 5. Open-loop mode (an open-loop approximation of load control)—vary V₁(V₂=0) in an open-loop manner in accordance with a predetermined blocked electrostatic force vs. time function while keeping3D piezoelectric actuator182 static. This is the traditional nanoindentation operating mode of Hysitron's three-plate capacitive transducer.
  • 6. Spring-force mode—do not actuate the electrostatic actuator34 (V₁=V₂=0) and measure the spring force that relates to the contact force while varying the differential voltage to thez segment188 of3D piezoelectric actuator182 to affect the indenter-sample separation. Disconnecting the electrostatic actuation circuitry fromelectrostatic actuator34 before executing this mode will eliminate spring force noise derived from electrostatic force noise. This mode is reminiscent of an AFM or Nanofactory's instrument attempting to conduct nanoindentation.

The following assumes that the relevant electrostatic force constant is calibrated rather than calculated from geometric parameters. Nanoindentation operating modes numbered 1, 2, and 5 in the above list require knowledge of κ_o, d_o, andkto calculate F_cbecausedisplaceable electrodes42 are displaced during the nanoindentation test (see Expression E.7 in conjunction with Expression E.5). Mode number 3 from the above list requires knowledge of κ_oand d_oto calculate F_c, but not k becausedisplaceable electrodes42 are suppressed from displacing during the nanoindentation test. The not obvious necessity of knowing both κ_oand d_oin the case of mode numbered 3 will be explained in greater detail below. Mode number 4 from the above list requires knowledge of a K_bcorresponding to the electrostatic force constant for the balanced condition to calculate F_c, but not k ord (the balanced condition's analog to d_o) becausedisplaceable electrodes42 are suppressed from displacing during the nanoindentation test; a contact force equation utilizing κ_bwill be provided in the next paragraph. Mode number 6 from the above list does not require knowledge of κ_oor d_obecause this mode does not involve generation of electrostatic force, but obviously requires the knowledge of k to calculate F_c. Of course, the above list is not exhaustive. For example, it is also possible to invoke modes involving variations in V₁and V₂that cause δ to change while keeping3D piezoelectric actuator182 static, but such modes are more complicated to calibrate than the others.

The following begins a detailed explanation of the novel advantages of the double-sided force-feedback control mode over the torque balance operation of the IFM. First, assumeelectrostatic actuator34 is endowed with perfectly balanced electrode gaps at V₁=V₂=0 whenconductive indenter62 is far removed from the sample. Next, assume the electrode gaps ofelectrostatic actuator34 remain balanced after equating both V₁and V₂to a bias voltage V_o(preferably 300V),conductive indenter62 still being far removed from the sample. Additionally, assume V₁=V_o+V_fband V₂=V_o−V_fbwhen using this nanoindentation operating mode, where V_fbis a fed-back adjustment to V₁and V₂, which is restricted to the range of ±V_o, and which keeps the electrode gaps ofelectrostatic actuator34 balanced in the presence of F_c. With this scenario, V_fbis zero whenconductive indenter62 is far removed from the sample, and is negative or positive when F_cis attractive or repulsive, respectively. Setting the sum of the electrostatic force owing to V₁, the electrostatic force owing to V₂, and F_cto zero yields the following Expression E.8 for the contact force:
F_c=4κ_bV_oV_fb  E.8;
which means F_cis a linear function of V_fb. In practice, achieving a high degree of linearity requires maintaining the electrode gaps of electrostatic actuator34 (rather than the electrode gaps of capacitive displacement sensor36) at the balanced condition, which is the motivation for utilizingelectrostatic actuator34 as an additional capacitive displacement sensor.

The following continues the detailed explanation of the novel advantages of the double-sided force-feedback control mode over the torque balance operation of the IFM. In the case of the IFM, it is the sum of the torques rather than of the forces that is directly pinned to zero by the action of the electrostatic-force-feedback controller. Keeping this in mind, let's examine the IFM sensor being controlled in a manner analogous to the double-sided force-feedback control mode of the present invention. With this assumption, setting the sum of the torques to zero (again assuming inherently balanced electrode gaps) yields Expression E.9 below:
F_c=4κ_bV_oV_fbL/L′  E.9;
where L is the moment arm from either electrostatic force to the torsion bar axis and L′ is the moment arm from the indenter to the torsion bar axis. Hence, the IFM also is capable of operating in a manner in which F_cis a linear function of V_fb. However, achieving linearity comes with a difficulty: the sum of the indenter-side electrostatic force κ_b(V_o−V_fb)², the non-indenter-side electrostatic force κ_b(V_o+V_fb)², and F_cis not kept at the initial sum of these forces equaling 2κ_bV_o². In fact, the change in the sum of these forces relative to 2κ_bV_o²is given by F_c+2κ_bV_fb²which clearly is nonzero in general. As a consequence, the torsion bars will deflect in a manner resulting in the electrode gaps uniformly expanding or collapsing, with the amount of this unintended deflection being dictated by the associated restoring force of the torsion bars equilibrating with the change in the sum of the electrostatic forces and F_c. The electrode gaps expanding or collapsing uniformly results in an atypical mechanical compliance not directly detectable by the IFM, and introduces error in the calculation of F_cbecause Expression E.9 assumes the electrode gaps to be invariant.

The following concludes the detailed explanation of the novel advantages of the double-sided force-feedback control mode over the torque balance operation of the IFM. As it turns out, the only way of eliminating the atypical source of mechanical compliance is to fix the non-indenter-side electrostatic force to κ_bV_o²and set L and L′ to be equal. With this configuration, Expression E.10 yields:
F_c=2κ_bV_oV_fb−κ_bV_fb²  E.10;
which means F_cis no longer a linear function of V_fb. Obviously, the double-side force-feedback control mode in combination with actuatable capacitive transducer30 (or in combination with any other nanoindentation transducer comprising a stacked three-plate electrostatic actuator, such as Hysitron's three-plate capacitive transducer, for example) is an improvement over any form of torque balance operation of the IFM.

The wide variety of nanoindentation operating modes feasible for use withcontrol system220 ofnanoindentation head180 are not equally worthy when conducting nanoindentation tests in a TEM. Reference 4 describes the overwhelming superiority of displacement control over load control if the goal is to investigate discrete deformation phenomena such as the onset of plasticity, likely an impetus for quantitative in-situ TEM nanoindentation experimentation. Furthermore, displacement control rather than load control provides nanoindentation data that can be directly compared to molecular dynamics simulations and finite element modeling of nanoindentation-induced deformation, also likely an impetus for quantitative in-situ TEM nanoindentation experimentation. Modes numbered 2-4 in the above list are variations of displacement control, but those numbered 3 and 4 require an additional displacement sensor dedicated to measuring the extension or contraction of3D piezoelectric actuator182 to achieve high penetration depth accuracy. Consequently, mode numbered 2 represents the simplest path to quantitative displacement-controlled force-displacement curves. However, modes numbered 3 and 4 are superior from the viewpoint of transducer control performance because it is easier to simply fend off forces attempting to deflectdisplaceable electrodes42 in comparison to meeting an indenter displacement demand ramp, as is the case withmode number 2. Mode number 3 does require V₁>0 before engaging a sample in order to have a range of V₁in reserve for fending off attractive forces acting onconductive indenter62.

Mode numbered 4 (the other force-feedback control mode) does not require a similar consideration on account of it being inherently bidirectional in terms of net electrostatic force, although this mode will involve a background V_fbto balance the electrode gaps ofelectrostatic actuator34 if these electrode gaps are not inherently balanced. The presence of a large background V_fbwill significantly alter the range of V_fbremaining to counter forces acting onconductive indenter62. A negative background V_fbis preferable over a positive one because a typical nanoindentation test involves attractive forces that pale in comparison to the maximum in repulsive force. This aspect should be considered when constructingactuatable capacitive transducer30.

As for load control,mode number 5 from the above list (an open-loop approximation of load control) provides an advantage over mode number 1 (true load control) in the sense that the former can be initiated from the out-of-contact condition, whereas the latter requires being in contact to achieve feedback loop closure. It is desirable to have the option of initiating nanoindentation tests from the out of condition (also a characteristic of modes numbered 2-4 and 6) in light of our quantitative in-situ TEM nanoindentation results revealing a single nanograin of aluminum plastically deforming upon first contact.Mode number 5, however, does have two distinct disadvantages in comparison tomode number 1. Firstly, in the case ofmode number 5, the achieved F_cwill not exactly match the desired F_c, the usually small difference being related to F_sand the dependence of F_eon δ. Secondly, open-loop modes of operation (mode number 6 included) do not provide an opportunity to tune a feedback loop to damp actuatablecapacitive transducer30 in the high-vacuum environment of a TEM. As will be demonstrated, an optimally tuned feedback loop dramatically decreases the settling time of actuatable capactive transducer30 in this very low damping medium.

As for mode number 6, it falls outside the domain of quantitative nanoindentation on account of the series loading configuration it adopts. Furthermore, this mode does not enable dictating either a well-defined penetration depth rate or a well-defined contact force rate, a significant drawback if testing rate sensitive materials. Further, this mode is subject to the well-known jump-to-contact phenomenon that can happen during initial sample approach. Further still, this mode necessitates an additional displacement sensor dedicated to measuring the extension or contraction of3D piezoelectric actuator182 to achieve the best possible performance. But in spite of these numerous difficulties, mode number 6 still is useful because it is the mode most capable of detecting extremely small forces, providing the electrostatic actuation circuitry is disconnected fromelectrostatic actuator34.

Switching between various nanoindentation operating modes during a nanoindentation test is a possibility. For example, it is feasible to start the nanoindentation test in the load control mode (mode number 1) to maintain F_cat a specific small repulsive value for the purpose of measuring the rate of positional drift, then switch to the displacement control mode (mode number 2) to detachconductive indenter62 from the sample by a specified distance, then reengage the sample in the displacement control mode (mode number 2) to the specific small repulsive value or to some other repulsive value, then switch to the load control mode (mode number 1) to increase F_cto the desired maximum load and to subsequently decrease F_cto the specific small repulsive value or to some other repulsive value, then switch to the displacement control mode (mode number 2) to detachconductive indenter62 from the sample by a specified distance. This scenario allows for data correction with regard to positional drift (see Reference 21), and provides data possibly showing attractive interaction forces during the reengagement step, and provides data for better establishing the position of the sample's surface which defines the zero point of the nanoindentation test (see Reference 21), and provides data possibly showing adhesive forces (also attractive) asconductive indenter62 detaches from the sample for the final time, while conducting the bulk of the nanoindentation test in the load control mode (mode number 1). Of course, V₁must be greater than zero before engaging the sample prior to the nanoindentation test in order to have enough V₁in reserve to be able to chase positional drift of either sign and to be able to guarantee the ability to detachconductive indenter62 from the sample. Here, engaging the sample prior to the nanoindentation test involves the use of3D piezoelectric actuator182 to displace actuatablecapacitive transducer30 towards the sample until achieving the specific small repulsive value.

The following Expression E.11 can be used to calculate the contact force for the case of V₁intentionally greater than zero before engaging the sample in conjunction with V₂=0 throughout the nanoindentation test:

$\begin{array}{cc}{F}_c=\frac{{\kappa }_o}{{\left[1-\left({\delta }^{\prime }+{\delta }_{\mathrm{offset}}\right)/d_o\right]}^2}{\left(V^{\prime }+V_{\mathrm{offset}}\right)}^2-\frac{{\kappa }_o}{{\left(1-{\delta }_{\mathrm{offset}}/d_o\right)}^2}{V}_{\mathrm{offset}}^2-k{\delta }^{\prime };& E\mathrm{.11}\end{array}$
where V_offsetis the value of V₁before engaging the sample, V′ is the change in V₁from V_offset, δ_offsetis the value of δ owing to V_offset, δ′ is the change in δ from δ_offset, and where the remaining parameters have been defined already. In the case of the single-sided force-feedback control mode (mode number 3), the value of V′ is whatever is necessary to maintain δ at zero. The necessity of knowing both κ_oand d_oin this case stems from the need to calculate the term

$\frac{{\kappa }_o}{{\left(1-{\delta }_{\mathrm{offset}}/d_o\right)}^2}$
for any chosen value of V_offset. The instrument's software treats V_offsetas an adjustable parameter to allow the user to balance having a sufficient reserve in V₁against shrinking the range of V′.

Returning to the jump-to-contact phenomenon,conductive indenter62 will jump into contact with the sample if the gradient of the attractive force acting onconductive indenter62 exceeds the spring constant of actuatablecapacitive transducer30. The occurrence of jump-to-contact prevents force-displacement measurement over the entire range of indenter-sample separation.Mode number 5 also is subject to the jump-to-contact phenomenon, whereas mode numbers 2-4 are stable against jump-to-contact on account of the displacement control they provide. However, no mode can stop atoms of the sample's surface from jumping into contact withconductive indenter62 if they desire to do so. As formode number 1, the jump-to-contact phenomenon is irrelevant becausemode number 1 requires being in repulsive contact before being initiated.

The combination ofnanoindentation head180, which comprisesactuatable capacitive transducer30 and3D piezoelectric actuator182,TEM holder203, andnanoindentation head180control system220 helps define a quantitative in-situ TEM nanoindenter. Numerous performance aspects of a built quantitative in-situ TEM nanoindenter were investigated in a JEOL JEM 3010 TEM located at NCEM/LBNL over the time period of Mar. 23-25, 2005. NCEM/LBNL is a facility of the Department of Energy and a confidentiality agreement is in place with this facility. Unless indicated otherwise, the performance results that follow were obtained in this particular TEM. Obviously, all components specified in the description of the performance results are built components.

To quantify baseline noise characteristics, out-of-contact force and displacement vs. time traces were acquired in a measurement bandwidth typical of nanoindentation tests. From these traces, the out-of-contact force noise floor was estimated to be 0.11 μN RMS while using the open-loop mode with V₁=0, and 0.16 μN RMS while using the displacement control mode with the demanded δ kept constant. From the same traces, the out-of-contact displacement noise floor was estimated to be 0.41 nm RMS while using the open-loop mode, and 0.48 nm RMS while using the displacement control mode. These values are considerably above the limits for thermally-driven mechanical noise in the same measurement bandwidth, yet are indicative of a high-performance nanoindenter. The out-of-contact noise floors were not affected by the status of the 300 kV electron beam (impinging the conductive indenter vs. turned off) or by the choice of magnification mode (low vs. high).

Use of the displacement control mode caused a moderate increase in the out-of-contact noise floors; however, this mode and the other modes invoking feedback were extremely beneficial in terms of improving the time to settle after encountering a transient disturbance.FIG. 10A illustrates an out-of-contact impulse-ring-down trace250 for the open-loop mode (V₁=0) with the vacuum pressure in the range of 10⁻⁷torr. Based on the exponential decay of the trace's envelope, the Q in high vacuum is 6000 in comparison to only 25 in an air environment. As a consequence, the elapsed time to a 99% settled displacement signal is an unacceptably long 66 s.FIG. 10B provides an out-of-contact step-response trace252 while using the displacement control mode with the vacuum pressure in the range of 10⁻⁷torr; a step change in the demanded δ initiated the step response. The benefit of closed-loop operation is clearly evident in that the elapsed time to a 99% settled displacement signal is reduced from an unacceptably long 66 s to a mere 13 ms.

A hand turning any of coarse positioning screws210 of theTEM holder200 was found to be a significant source of potentially damaging transients. On several occasions,conductive indenter62 visibly damaged the sample while coarse positioning, the result of high-amplitude ringing in high vacuum set off by the action of the hand. Of note, all such occurrences corresponded to using the open-loop mode. Apparently, closed-loop control prevented large swings in indenter displacement even during the rough act of coarse positioning. Closed-loop control also suppressed ringing following a sudden change in how a sample responded to a nanoindentation test.

The stability of the natural state ofdisplaceable electrodes42 against rotation ofTEM holder200 about its central axis was tested over the physically possible range of 0-28°. The change in the displacement signals was only 46.8 nm over the full range of rotation, which indicated an extremely horizontal alignment with respect to gravity. The stability of the natural state also was tested against the status of the electron beam. The electron beam impingingconductive indenter62 did not affect the displacement signals relative to their values with the electron beam turned off. However, the displacement signals were noticeably impacted by the choice of magnification mode. Switching from low to high magnification mode reproducibly caused the displacement signals to shift by an amount corresponding to 1.03 μm towards the electron beam. Fortunately, the shift was invariant as long as the magnification mode remained unchanged.

A shift by 1.03 μm is not unacceptable, but does require onsite re-determination of the electrostatic force calibration function for certain nanoindentation operating modes. The instrument's software possesses an algorithm designed to optimize the electrostatic force calibration function so that post-shift, out-of-contact force-displacement curves will yield the proper value for k. A shift significantly much greater than 1.03 μm would be intolerable, especially for the case of the double-sided force-feedback control mode.

The displacement signals in the low magnification mode were comparable to their values for horizontal alignment outside the TEM. This observation is consistent with a weak to nonexistent local magnetic field when in the low magnification mode, and a strong local magnetic field when in the high magnification mode. Trace levels of ferromagnetic impurities in components of actuatable capacitive transducer30 likely participated in the coupling to the magnetic field. The titanium shaft ofconductive probe60 possesses by far the highest ferromagnetic content in terms of concentration, iron impurities at the level of 0.3 wt %, and in terms of total number of ferromagnetic atoms. Hence, an ultrapure titanium shaft might substantially reduce coupling to the magnetic field.

FIG. 11A illustrates one embodiment of anelectrical configuration260 found to be compatible with the JEOL JEM 3010 TEM for bleeding charge fromconductive indenter62. As can be seen inFIG. 11A,conductive indenter62, the remainder ofconductive probe60, conductive threadedrod48, and aprobe wire262 soldered to theprobe wire tab56 in intimate electrical contact with conductive threadedrod48 form an electrical path toTEM holder200.FIG. 11A also shows asample264 electrically connected toTEM holder200 to ensure that the sample andconductive indenter62 are nominally at the same electrical potential, via good electrical continuity betweensample clamp212 and the point at which the probe wire attaches toTEM holder200.Probe wire262 must be highly flexible in order to not impede the motion ofdisplaceable electrodes42.

TEM holder200 could not be grounded to controlsystem200 ofnanoindentation head180 as doing so sounded an alarm originating from the TEM. However, electrically connecting theconductive transducer body32 of actuatable capacitivetransducer30 andground planes84 to the ground ofcontrol system220 did not sound the alarm because these components were kept electrically isolated fromTEM holder200. Apparently, electrically connectingTEM holder200 to the ground ofcontrol system220 is interpreted by the TEM as a crash ofTEM holder200 into a pole piece.

FIGS. 11B and 11C show force-displacement curves270 and272 while using the displacement control mode, which correspond toconductive indenter62 first approaching then withdrawing from the tip of a plank-type silicon AFM cantilever while the TEM imaged bothconductive indenter62 and the tip of the cantilever. The curve inFIG. 11B illustrates the detrimental impact of not electrically connectingconductive indenter62 to a charge sink of any type, whereas the curve inFIG. 11C is an example of a proper mechanical response. Measuring a proper mechanical response required bothconductive indenter62 and the AFM cantilever (product no. NSC15/No Al from μmasch) being nominally at the same electrical potential.

InFIG. 11B, the significant attractive (negative) forces seen in the initial portion of the approach segment likely are the consequence ofconductive indenter62 and the AFM cantilever absorbing different amounts of charge from the electron beam. The subsequent lack of attractive forces throughout the withdrawal segment likely is evidence for charge equilibration once repulsive contact (yielding positive forces) has been made. Interestingly, the observation of at least two discrete decreases in attractive force during the initial portion of the approach segment is suggestive of discrete charge transfer events occurring prior to making repulsive contact.FIG. 11C, in comparison, does not show significant attractive forces over any portion of the curve. Moreover, the approach segment data and the withdrawal segment data inFIG. 11C are virtually identical. Apparently,TEM holder200 serves as a sufficient charge sink even when not electrically connected to the ground ofcontrol system220 ofnanoindentation head180.

To ascertain the ability of actuatable capacitive transducer30 to maintain its metrological accuracy in the TEM environment, a number of force-displacement curves while using the displacement control mode were acquired withconductive indenter62 against the tip of the AFM cantilever while imaging with the TEM. The initial slope of these force-displacement curves was consistent with an AFM cantilever spring constant of 50.6±0.8N/m at the tip location. In comparison, a value of 50.9N/m at the tip location was obtained by inputting the AFM cantilever's dimensions (measured from SEM images) into the well-known cantilever bending equation. The high level of agreement between measured and calculated AFM cantilever spring constants indicated the TEM environment did not impact the metrological accuracy of actuatablecapacitive transducer30.

The following is an example of methodology preceding quantitative in-situ TEM nanoindentation tests on wedge-shaped samples, such as wedge-shapedsample264 depicted inFIG. 11A, which have a plateau generally in the range of 100 nm in width and macroscopic dimension in length. First,TEM holder200 is translated and rotated to achieve optimized TEM images ofsample264. Next, the TEM's magnification is adjusted to provide a large enough field of view such that bothconductive indenter62 andsample264 can be seen at the same time. Next, coarse positioning screws210 ofTEM holder200 are adjusted to bringconductive indenter62 close enough to sample264 to be well within the range of motion of3D piezoelectric actuator182, while adjusting the TEM's magnification as needed. Any of the variations of displacement control can be used during coarse positioning to prevent large swings ofdisplaceable electrodes42 in response to the action of the hand adjusting coarse positioning screws210. Next,3D piezoelectric actuator182 is used to positionconductive indenter62 to within a nanoscale distance to a point on the plateau centered with respect to the plateau's width, again adjusting the TEM's magnification as needed, The desired nanoindentation operating mode, usually one of the variations of displacement control, can be selected during this process of fine positioning. Next, the nanoscale gap betweenconductive indenter62 and the plateau is observed for a period of time to ensure that it is stable. Once found to be stable, the nanoindentation test is initiated to indent the selected point on the plateau centered with respect to the plateau's width. Conducting a nanoindentation test in the load control mode (mode number 1) requires using3D piezoelectric actuator182 to placeconductive indenter62 in minimal repulsive contact with the plateau before initiating the nanoindentation test.

The following is a first example of quantitative in-situ TEM nanoindentation results that demonstrate the quantitative in-situ TEM nanoindenter's capability of investigating fundamental aspects of nanoscale material deformation.FIGS. 12A and 12B provide two examples of force-displacement curves280 and282 corresponding to a boron-doped diamond indenter of the Berkovich geometry indenting a nanograin of an aluminum film deposited on a wedge-shaped, single-crystal silicon substrate.Curve280 inFIG. 12A was acquired while using the displacement control mode, whereascurve282 inFIG. 12B was acquired while using the single-sided force-feedback control mode. Bothcurves280 and282 are dominated by repulsive forces, but both indicate relatively strong attractive adhesive forces during the final act of withdrawingconductive indenter62 from the aluminum nanograin.

Signals digitized during a nanoindentation test can include signals indicative of electrostatic actuation voltage, signals indicative of displaceable electrode displacement, and a signal indicative of the extension or the contraction ofz segment188 of3D piezoelectric actuator182. Time also is recorded. The TEM images provided inFIG. 12C correspond to twovideo frames284 and286 extracted from a stream of TEM images recorded during the process of acquiring the force-displacement curve280 inFIG. 12A. Lefthand video frame284 ofFIG. 12C shows the aluminum nanograin about to be indented to be initially dislocation free, whereas righthand video frame286 ofFIG. 12C shows that dislocations confined to the aluminum nanograin on account of a difficulty in traversing the grain boundary have been nucleated and multiplied during the process of nanoindentation.

Focusing on force-displacement curve280 ofFIG. 12A, there are several discrete load drops that occur during the process of increasing the penetration depth, where each discrete load drop corresponds to sudden stress relaxation accompanying a sudden change in the aluminum nanograin's subsurface dislocation structure, as indicated by time correlation of the force-displacement curve to the recorded stream of TEM images. This particular experimental result is the first to conclusively link discrete load drops to discrete dislocation nucleation and multiplication events. However, surprisingly, the first large discrete load drop, indicated at290, is not the one associated with the onset of plasticity, an observation at odds with the belief of many researchers. Instead, the onset of plasticity is coincident with the small force transient, indicated at292. Video frames284 and286 provided inFIG. 12C are sequential video frames of this initial dislocation nucleation and multiplication event. The conclusion reached here would not have been possible without having both a force-displacement curve and an associated time-correlated stream of TEM images.

As for force-displacement curve282 ofFIG. 12B, it corresponds to a different aluminum nanograin, yet is similar to force-displacement curve280 ofFIG. 12A in terms of overall characteristics. However, force-displacement curve282 ofFIG. 12B is obviously an improvement over force-displacement curve282 ofFIG. 12A in terms of transducer control performance. For example, the discrete load drops are more crisp incurve282 ofFIG. 12B. Unfortunately, the lack of a displacement sensor dedicated to measuring the extension or the contraction ofz segment188 of3D piezoelectric actuator182 deems force-displacement curve282 ofFIG. 12B not fully quantitative, although3D piezoelectric actuator182 is found to behave more ideally in high vacuum than in air.

The following is a second example of quantitative in-situ TEM nanoindentation results that demonstrate the quantitative in-situ TEM nanoindenter's capability of investigating fundamental aspects of nanoscale material deformation.FIG. 13A provides a force-displacement curve300 corresponding to the sameconductive indenter62 indenting an initially dislocation-free section of the plateau of a wedge-shaped, single-crystal silicon sample not having a film. This nanoindentation test was run in the displacement control mode, and involved a loading segment at a constant displacement rate, followed by a holding segment at a constant penetration depth, followed by an unloading segment at a constant displacement rate. The corresponding time-correlated stream of TEM images indicated an initial period of elastic contact followed by continuous dislocation activity during the remainder of the loading segment, but in contrast to the aluminum nanograins, load drops were not observed.

During the holding segment, stress relaxation gradually occurred even though both the contact area and the nanoindentation-induced dislocation structure seemed to be static. Nothing noteworthy occurred during the unloading segment until experiencing a strong attractive adhesive force (35 μN in magnitude) during the final act of withdrawing the conductive indenter from the sample. At this point,conductive indenter62 was kicked out suddenly from the sample which forced the control loop to fight back to recover the proper value of displacement in time. This kick-out event is indicated inFIG. 13aby the sequence of arrows. Finally, one more kick-out event occurred before completing the unloading segment, again starting from an attractive adhesive force. The corresponding time-correlated stream of TEM images confirmed the kick-out events being rather violent in nature.

FIG. 13B provides apost-mortem TEM image302 of the residual deformation zone as well as three post-mortem electron diffraction patterns.Diffraction pattern304 in the lower left hand corner corresponds to the diamond cubic crystal structure of pristine silicon,nanobeam diffraction pattern306 in the upper left hand corner also corresponds to the diamond cubic crystal structure but comes from the heavily dislocated region of the residual deformation zone, andnanobeam diffraction pattern308 of amorphous character in the upper right hand corner comes from the surface pile not present before the nanoindentation test. Apparently, tensile stresses associated with adhesive forces were enough to trigger sudden volume-expanding phase transformations from plastically-deformed, diamond-cubic silicon to amorphous silicon. This particular experimental result raises the interesting possibility of a method that entails viewing/recording the evolution of the nanobeam diffraction pattern throughout the nanoindentation test in order to monitor the local crystal structure as a function of the force-displacement curve.

The following concludes the description of the in-TEM performance results:

• • 1.Actuatable capacitive transducer30 was stable against the snap-to-contact instability over the software-permitted displacement range of 5 μm.
  • 2.Actuatable capacitive transducer30 was stable against the spark-gap instability over the range of electric field strength needed to conduct the tests.
  • 3. Corona discharge was not observed. Neither actuatable capacitivetransducer30 nor 3D piezoelectric actuator182 (also a high voltage device) received power until achieving high vacuum.
  • 4. TEM images did not provide evidence forconductive indenter62 charging up even when an electrical path fromconductive indenter62 toTEM holder200 was not provided. This observation suggests force-displacement curves are more sensitive to charging than TEM images.
  • 5. In general, the quantitative in-situ TEM nanoindenter did not exhibit positional drifts large enough to be detected at the magnifications necessary for the tests. Drifting relative to the TEM image's field of view can be ascertained by directly observing the position ofconductive indenter62 and the position of the sample during periods of idle.
  • 6. Although a value for the load frame stiffness was not determined, nothing indicated a load frame stiffness problem.
  • 7. Pumping down the fully-assembled TEM holder after plasma cleaning took approximately 1 hour. In comparison, pumping down theTEM holder200 prior to receiving the assembly comprised of theinternal tube206,3D piezoelectric actuator182, and actuatablecapacitive transducer30 took only about 5 minutes. Although a pump-down time of approximately 1 hour is not intolerable, adding vents to the internal tube should result in an improvement.
  • 8. It is not trivial to properly positionconductive indenter62 with respect to a wedge-shaped sample's plateau because the electron beam transmits through the sample andconductive indenter62 regardless of whetherconductive indenter62 or the sample is in the foreground relative to the other. A scanning probe microscopy method of imaging in the manner of an AFM but using the indenter rather than a tip on a cantilever, to image the topography of the plateau and the transitions to the sample's side slopes, would be advantageous because such an image could be used as a guide for refining the position ofconductive indenter62 with respect to the plateau, although the process of imaging might damage the sample. In the event of sample damage, the three-dimensional topography image could be used to predict how much to offset3D piezoelectric actuator182 in all three spatial dimensions to properly positionconductive indenter62 with respect to a nearby undamaged section of the plateau without contacting the sample. Post-test imaging in the manner of an AFM also enables highly complementary three-dimensional and plan-view images of the residual deformation zone. Imaging in the manner of an AFM could be based on feedback involvingz segment188 of3D piezoelectric actuator182 to maintain either a constant spring force if actuatable capacitivetransducer30 is passive during imaging or a constant transducer control effort if actuatable capacitivetransducer30 is active during imaging. The former involves a single feedback loop, whereas the latter involves one feedback loop nested in another, the transducer control loop being the nested loop.

The following begins a description of several embodiments of the present invention. In a preferred embodiment of actuatablecapacitive transducer30,electrostatic actuator34 rather than thecapacitive displacement sensor36 is closest toconductive indenter62. In an alternative embodiment of actuatablecapacitive transducer30,capacitive displacement sensor36 rather thanelectrostatic actuator34 is closest toconductive indenter62. An advantage ofelectrostatic actuator34 being closest toconductive indenter62 is that such an arrangement effectively shortens a length ofcoupling shaft46 which is potentially under high load. However, it has been determined that force-displacement curves do not noticeably depend on whetherelectrostatic actuator34 orcapacitive displacement sensor36 is closest toconductive indenter62.

In the preferred embodiment of actuatablecapacitive transducer30, having both first and secondmulti-plate capacitors34 and36 functioning as capacitive displacement sensors might seem redundant at first glance. The reason forelectrostatic actuator34 also functioning as a capacitive displacement sensor has been explained, but not the reason for having a multi-plate capacitor functioning solely as a capacitive displacement sensor. Prior-art actuatable capacitive transducers have been used to conduct dynamic forms of nanoindentation testing as well as dynamic forms of imaging in the manner of an AFM (see References 37-39). However, it is difficult to suppress an oscillatory electrostatic actuation voltage from feeding through, i.e., a portion of the oscillatory electrostatic actuation voltage will appear in the displacement signal if the displacement signal originates from the multi-plate capacitor experiencing the oscillatory electrostatic actuation voltage. This undesirable dynamic feedthrough effect increases in severity with increasing oscillation frequency. Hence, a multi-plate capacitor functioning solely as a capacitive displacement sensor provides means for obtaining a displacement signal free of dynamic feedthrough. This explanation leads to another alternative embodiment of actuatablecapacitive transducer30, wherein one multi-plate capacitor functions solely as a capacitive displacement sensor and another multi-plate capacitor functions solely as an electrostatic actuator, if one is willing to forego the double-sided force-feedback control mode.

Yet another alternative embodiment of actuatable capacitive transducer30 involves both first and secondmulti-plate capacitors34 and36 functioning as electrostatic actuators to increase the load capacity, and at least one of first and secondmulti-plate capacitors34 and36 functioning as a capacitive displacement sensor, if one is willing to forego dynamic forms of nanoindentation testing/imaging not corrupted by dynamic feedthrough. Of course, it is also feasible to incorporate more than two multi-plate capacitors intoactuatable capacitive transducer30 to yield many possible combinations of multi-plate capacitors functioning as electrostatic actuators and capacitive displacement sensors. Any capacitor being used solely as an electrostatic actuator can be a two-plate capacitor rather than a three-plate type of a multi-plate capacitor.

In the preferred embodiment of actuatablecapacitive transducer30, conductive threadedrod48 is utilized to electrically connectconductive probe60 to the remainder of the electrical path responsible for bleeding charge fromconductive indenter62. It is possible to eliminate the need for conductive threadedrod48 being integral to the electrical path if theprobe wire262 is electrically connected toconductive probe60 instead, but this is a far more cumbersome solution than the one implemented. Nevertheless, attaching a probe wire toconductive probe60 is within the scope of the present invention. Eliminating the capacitive displacement sensing function ofelectrostatic actuator34 would allowdisplaceable electrode42 ofelectrostatic actuator34 to be grounded. Conductive threadedrod48 in electrical contact with the grounded displaceable electrode would preventconductive indenter62 from charging up. However, in the case of the JEOL JEM 3010 TEM, this would requiresample clamp212, being electrically isolated fromTEM holder200, to be grounded as well and to avoid sounding the TEM's alarm in the event the electrical conductivity of the indenter-sample contact increased sufficiently. Furthermore, electron beam current passing throughdisplaceable electrode42 ofelectrostatic actuator34 might cause enough noise to be evident in force-displacement curves. Electrically isolatingsample clamp212 fromTEM holder200 does raise the interesting possibility of electrically biasing the sample relative toconductive indenter62 to measure the electrical conductivity of the indenter-sample contact. But this would be problematic ifconductive indenter62 was electrically connected todisplaceable electrode42 ofelectrostatic actuator34 because thendisplaceable electrode42 would be increasingly shorted to the sample bias as the electrical conductivity of the indenter-sample contact increased.

Other feasible but non-exhaustive modifications to embodiments of the present invention described herein include significantly shortening the portion ofcoupling shaft46 external toconductive transducer body32, pairing each spring ofsprings44 with a mirror image spring, adding a lock-in amplifier to controlsystem220, and motorizing coarse positioning screws210. In one scenario, the preferred embodiment of actuatable capacitive transducer30 could be used for horizontal applications outside a TEM, but it would not be suitable for vertical applications on account of gravity's effect on the relatively high sprung mass. Significantly shorteningcoupling shaft46 to sufficiently reduce the sprung mass would allow actuatablecapacitive transducer30 to be used in vertical applications, although this likely would render actuatablecapacitive transducer30 useless in a TEM. Pairing each spring ofsprings44 with a mirror image spring would eliminate any tendency ofdisplaceable electrodes42 to rotate while being displaced, but these additional springs would complicate achieving a relatively low overall spring constant. Adding a lock-in amplifier to controlsystem220 to measure the amplitude and the phase shift of the oscillatory component of the displacement signal ofcapacitive displacement sensor36 during dynamic excitation would facilitate dynamic forms of nanoindentation testing/imaging. Motorizing coarse positioning screws210 would eliminate the large transients caused by the action of the hand turning the screws, and would enable motor-assisted hunting of the sample's surface in the manner of an AFM. This concludes the description of several embodiments of the invention in addition to the preferred embodiment.

Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent implementations may be substituted for the specific embodiments shown and described without departing from the scope of the present invention. This application is intended to cover any adaptations or variations of the specific embodiments discussed herein. Therefore, it is intended that this invention be limited only by the claims and the equivalents thereof.

Claims (27)

What is claimed is:

1. A method of quantitative nanoindentation combined with transmission electron microscopy comprising:

indenting a sample by actuating an actuatable capacitive transducer, wherein actuating includes adjusting voltages supplied to the actuatable capacitive transducer;

bleeding electrical charge from an electrically conductive indenter of the actuatable capacitive transducer, the charge resulting from an electron beam impinging the electrically conductive indenter, via an electrically conductive path in electrical communication with the electrically conductive indenter, the electrically conductive indenter and electrically conductive path being electrically isolated from other components of the actuatable capacitive transducer;

recording signals required to generate a representation of a force-displacement relationship; and

recording a stream of transmission electron microscopy images illustrating one or more aspects of indenting the sample.

2. The method ofclaim 1, wherein the representation of a force-displacement relationship comprises a force-displacement curve.

3. The method ofclaim 2, wherein the force-displacement curve comprises a contact force versus a penetration depth curve.

4. The method ofclaim 1, further comprising recording a time while indenting the sample to generate a representation of a force-time relationship.

5. The method ofclaim 4, wherein the representation of a force-time relationship comprises a contact force versus time curve.

6. The method ofclaim 1, further comprising recording a time while indenting the sample to generate a representation of a displacement-time relationship.

7. The method ofclaim 6, wherein the representation of a displacement-time relationship comprises a penetration depth versus time curve.

8. A method of quantitative nanoindentation combined with transmission electron microscopy comprising:

indenting a sample by actuating an actuatable capacitive transducer;

bleeding electrical charge from an electrically conductive indenter, via an electrically conductive path in electrical communication with the electrically conductive indenter, the electrically conductive indenter and electrically conductive path being electrically isolated from other components of the actuatable capacitive transducer;

controlling a displacement resulting from actuating the actuatable capacitive transducer;

recording signals required to generate a force-displacement curve; and

recording a stream of transmission electron microscopy images illustrating one or more aspects of indenting the sample.

9. The method ofclaim 8, wherein the force-displacement curve comprises a contact force versus a penetration depth curve.

10. The method ofclaim 8, wherein controlling the displacement involves feedback means and optionally feedforward means.

11. The method ofclaim 8, further comprising recording a time while indenting the sample to generate a force-time curve and/or a displacement-time curve.

12. A method of quantitative nanoindentation combined with transmission electron microscopy comprising:

indenting a sample by actuating an actuatable capacitive transducer;

bleeding electrical charge from an electrically conductive indenter of the actuatable capacitive transducer, via an electrically conductive path in electrical communication with the electrically conductive indenter, the electrically conductive indenter and electrically conductive path being electrically isolated from other components of the actuatable capacitive transducer;

controlling a contact force resulting from indenting the sample;

recording signals required to generate a curve representative of the contact force versus a penetration depth; and

recording a stream of transmission electron microscopy images illustrating one or more aspects of indenting the sample.

13. The method ofclaim 12, wherein controlling the contact force involves feedback means and optionally feedforward means.

14. The method ofclaim 12, further comprising recording a time while indenting the sample to generate a curve representative of the contact force versus the time and/or a curve representative of the penetration depth versus the time.

15. A method of quantitative nanoindentation combined with transmission electron microscopy comprising:

indenting a sample by actuating a piezoelectric actuator while operating an actuatable capacitive transducer in a single-sided force-feedback control mode;

bleeding electrical charge from an electrically conductive indenter of the actuatable capacitive transducer, via an electrically conductive path in electrical communication with the electrically conductive indenter, the electrically conductive indenter and electrically conductive path being electrically isolated from other components of the actuatable capacitive transducer;

recording signals required to generate a contact force versus penetration depth curve; and

recording a stream of transmission electron microscopy images illustrating one or more aspects of indenting the sample.

16. The method ofclaim 15, further comprising recording a time while indenting the sample to generate a contact force-time curve and/or a penetration depth-time curve.

17. The method ofclaim 15, wherein operating the actuatable capacitive transducer in the single-sided force-feedback control mode generally prevents a displaceable electrode of the actuatable capacitive transducer from displacing relative to a transducer body of the actuatable capacitive transducer.

18. A method of quantitative nanoindentation combined with transmission electron microscopy comprising:

indenting a sample by actuating a piezoelectric actuator while operating an actuatable capacitive transducer in a double-sided force-feedback control mode;

recording signals required to generate a force-feedback curve;

recording a stream of transmission electron microscopy images illustrating one or more aspects of indenting the sample, wherein operating the actuatable capacitive transducer in the double-sided force-feedback control mode generally prevents a displaceable electrode of the actuatable capacitive transducer from displacing relative to a transducer body of the actuatable capacitive transducer and wherein recording signals includes recording a feedback voltage ideally proportional to a contact force.

19. The method ofclaim 18, further comprising recording a time while indenting the sample to generate a force-time curve and/or a displacement-time curve.

20. A method of quantitative nanoindentation combined with transmission electron microscopy comprising:

indenting a sample by actuating an actuatable capacitive transducer;

controlling a contact force resulting from indenting the sample whenever the contact force is above a specified contact force and controlling a displacement resulting from actuating the actuatable capacitive transducer whenever the contact force is below the specified contact force;

recording signals required to generate a contact force versus penetration depth curve; and

recording a stream of transmission electron microscopy images illustrating one or more aspects of indenting the sample.

21. The method ofclaim 20, further comprising recording a time while indenting the sample to generate a contact force versus time curve and/or a penetration depth versus time curve.

22. The method ofclaim 20, wherein controlling the contact force and/or controlling the displacement involves feedback means and optionally feedforward means.

23. A method of quantitative nanoindentation combined with transmission electron microscopy comprising:

indenting a sample;

bleeding electrical charge form an electrically conductive indenter, via an electrically conductive path in electrical communication with the electrically conductive indenter, the electrically conductive indenter and electrically conductive path being electrically isolated from other components including an actuatable capacitive transducer;

recording signals required to generate a contact force versus a penetration depth curve; and

recording a stream of electron diffraction patterns illustrating one or more aspects of indenting the sample.

24. The method ofclaim 23, further comprising recording a time while indenting the sample to generate a contact force versus time curve and/or a penetration depth versus time curve.

25. A method of positioning an indenter relative to a substantially wedge-shaped sample having a plateau, a first inclined sidewall, and a second inclined sidewall, the method comprising:

using the indenter to generate a scanning probe microscopy topography image illustrating a portion of the plateau, a portion of the first inclined sidewall, and a portion of the second inclined sidewall;

determining a three-dimensional spatial orientation of the plateau from the image;

determining a width of the plateau from the image; and

positioning the indenter relative to the plateau using the width of the plateau and the three-dimensional spatial orientation of the plateau as a guide.

26. The method ofclaim 25, wherein positioning the indenter relative to the plateau places the indenter in close proximity to or in contact with the plateau at a location illustrated in the image.

27. The method ofclaim 25, wherein positioning the indenter relative to the plateau places the indenter in close proximity to or in contact with the plateau at a location not illustrated in the image.

Images